A2 and AS Level Physics Notes

A level Physics notes By Anthony Cameron

Table of Contents Unit 1: Mechanics and Radioactivity................................................................................................... 2 Rectilinear motion............................................................................................................................2 Forces and moments........................................................................................................................ 2 Dynamics......................................................................................................................................... 3 Mechanical energy........................................................................................................................... 3 Radioactive decay and the nuclear atom..........................................................................................4 Unit 2: Electricity and thermal physics................................................................................................ 6 Electric current and potential difference..........................................................................................6 Electrical circuits............................................................................................................................. 9 Heating matter................................................................................................................................10 Kinetic model of matter................................................................................................................. 10 Conservation of energy.................................................................................................................. 11 Unit 3A Astrophysics......................................................................................................................... 12 A1 Observing stars.........................................................................................................................12 A2 The lives of stars...................................................................................................................... 14 Unit 4: Waves and our universe......................................................................................................... 16 Circular motion and oscillations.................................................................................................... 16 Waves.............................................................................................................................................18 Superposition of waves.................................................................................................................. 20 Quantum phenomena..................................................................................................................... 22 The expanding universe................................................................................................................. 26 Unit 5: Fields and forces.....................................................................................................................28 Gravitational fields........................................................................................................................ 28 Electric fields................................................................................................................................. 29 Capacitance.................................................................................................................................... 30 Magnetic fields.............................................................................................................................. 32 Simple Differences between Electric and Magnetic fields....................................................... 32 Electromagnetic induction............................................................................................................. 34 Unit 6: Synthesis.................................................................................................................................36 Analogies in physics...................................................................................................................... 36 Accelerators................................................................................................................................... 38 Appendix 1 – Uncertainty and error................................................................................................... 42 Appendix 2 – AS and A2 Experiment Diagrams............................................................................... 42 Experiments – Units 1 and 2..........................................................................................................42 Experiments – Units 4 and 5..........................................................................................................48 Appendix 3 – Units and symbols........................................................................................................51 Base SI units ................................................................................................................................ 51 Common derived units...................................................................................................................51 Symbols and their units..................................................................................................................51 Appendix 4 – Metric prefixes.............................................................................................................52 Common metric prefixes at A-level...............................................................................................52 All Other metric prefixes; common, rare and unused....................................................................52 Appendix 5 – Formula sheet...............................................................................................................53 Alphabetical index..............................................................................................................................55

Anthony Cameron

A level Physics notes;

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Unit 1: Mechanics and Radioactivity Rectilinear motion 1.1 Kinematics v=uat 1 s=ut at 2 2 2 2 v =u 2as 1 s= uv t 2

u=initial velocity v=final velocity s=displacement a=acceleration t =time

1.2 Graphical interpretation i.e. Unit y/x is represented by gradient Unit xy is represented by area of graph

Measurement of the acceleration of free fall. A method involving a body in free fall is expected. Steel ball is dropped and time and distance are measured. From this acceleration is calculated

On a distance – time graph, the gradient is the velocity (distance/time)

1.3 Projectiles Vertical and horizontal motion are two separate components that contribute to the overall motion. A projectile projected horizontally will still fall downwards at the same rate as one falling with no horizontal movement.

Forces and moments 1.4 Force interpreted as a push or a pull and identified as the push or pull of A on B. ALL forces either push or pall on an object. The gravitational force (the force between two masses) applied to a body is called weight and is equal to the product of mass and the acceleration due to gravity (Weight = mg) Electrostatic force – force between two charged objects Electromagnetic force – force between two charged objects (includes electrostatic force) Nuclear forces – Forces that hold the nucleus of atoms together Contact force – reaction to contact between two objects Normal reaction force – Reaction to weight, equal magnitude yet opposite direction Frictional force – Force between two objects that opposes motion Drag – force exerted by a fluid or gas which resists the movement of an object through that fluid Lift – Force that lifts an object 1.5

Free body force diagrams

1.6 Newton's First Law of motion A body will remain at rest or continue to move with a constant velocity as long as the forces on it are balanced. Reluctance to change velocity is the inertia of the body. Inertia is proportional to mass 1.7 Newton's Third law of motion Every action has an equal and opposite reaction 1.8 Moments about a point Moment = downward component of force multiplied by perpendicular distance Principle of moments. For a system to stay in equilibrium, the sum of the anticlockwise moments must equal the sum of the clockwise moments about that point. Anthony Cameron


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1.9

Density mass m Density= = volume V Solids are rigid, gases and liquids are fluid Measure mass using scales, measure volume by displacement of water

Dynamics 1.10 Linear momentum p=mv Momentum is the product of mass and velocity Principle of the Conservation of momentum – The total Momentum before a collision will equal the total momentum after the collision 1.11 Newton’s second law Newton's second law – Force equals the rate of change of momentum An Impulse is a change of momentum

mv−u t I=Ft=mv−u F=

Newton's three laws of motion 1) Law of inertia - A body will only accelerate if the forces acting on it are unbalanced Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed  mv 2) Law of acceleration - F=d dt The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction 3) Law of reciprocal actions – Each reaction has an equal and opposite action All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction Mechanical energy 1.13 Work done and energy transfer Work done = average applied force multiplied by the distance moved in the direction of the force. W = Fx 1.14

K.E. and G.P.E. 1 Kinetic energy= mv2 2 Gravitational potential energy=mgh

It can be assumed that for calculations involving heights close to the Earth's surface, g will equal 9.81 ms-2 and so: ΔE = mgΔh

1.15 Principle of the conservation of energy Energy may not be created or destroyed only transferred Energy will be conserved i.e. KE1 + GPE1 = KE2 + GPE2 An elastic collision is where all KE is conserved Efficiency = useful output/input 1.16

Power

Power is the rate of energy transfer (or of work done)

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P=

W =F v t

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Radioactive decay and the nuclear atom 1.17 The existence and nature of radioactive emissions Radioactivity is the spontaneous disintegration of the atom's nucleus, with the consequent emission of particles and energy from the atom Background radiation can come from; space, big bang, rocks (radon), carbon, et cetera 1.18 Properties of α, β+, β– and γ radiation and corresponding disintegration processes α (alpha) radiation These are high-speed helium nuclei They are very ionising, as they readily interact, but not have a very weak penetration, this is due to there large size. Therefore they are most dangerous when ingested as normally the can not penetrate far through skin Alpha radiation is used in smoke detectors – a stream of a particles carry a current over a short space of air. In the presence of smoke this is blocked off, so the current stops and an alarm will sound. 237 Np  233 Pa 4  Example 93 91 2 β (beta) radiation Less massive, less ionising but more penetrating then α β- consists of one electron and β+ of its opposite, a positron. Hence they annihilate each other on interaction, releasing energy proportional to there mass (E = mc2) βneutron → Proton + electron β+ proton → neutron + positron γ (gamma) radiation Composed of an EM wave Most penetrating but least ionising Emitted if there is excess energy after an α or β particle have been emitted. 1.19 Stable and unstable nuclei Nucleon number (atomic mass) is approximately equivalent to the number of protons and neutrons in the nucleus of the atom, the proton number is the number of protons in the nucleus of the atom. 237 93

Np This neptunium atom has a nucleon number of 237 and a proton number of 93 so it has 93 protons, 144 neutrons (144 is the difference between 237 and 93). If two atoms have the same number of protons but a different number of neutrons (hence different atomic mass), then they are isotopes of the same element. 1.20 Radioactivity as a random process Activity = λN N – number of nuclei λ – decay constant (s-1) - proportion of N that decays in on second Radioactive decay Radioactive material will decay at an exponential rate Half life is considered the time taken for the activity of a radioactive sample to drop its original value. This is also the time taken for half of the unstable nuclei in a radioactive sample to decay. hence ln 2 0.69 t 1 =Half life= ≈   2 Anthony Cameron


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1.21 The nuclear atom In elastic scattering, alpha particles are fired at gold leaf, most of the particles pass though however some are deflected back at an angle greater than 90o. Deep inelastic scattering involves firing a high energy electron at a proton. If the electron is low energy the proton recoils and the electron is elastically scattered. However with high energy electrons the scattering is deep and inelastic, proving the existence of protons being made up of a smaller differently charged particles. Geiger muller tube, for each ionising event of the argon and halogen gas mixture (inside the tube) a current passes through the tube and is recorded

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Unit 2: Electricity and thermal physics Electric current and potential difference 2.1 Charge and Current Charge (Q) Current as rate of flow of charge. I=

Q t

The sum of a current entering a point is equal to the sum of the currents leaving that point.1 Drift velocity The electrons in a metal don't just travel in one direction, they move in all directions more or less randomly. Their speed is very fast perhaps 100'000 m/s. When you add a battery or power supply this causes the random motion to be not quite random. There is a trend of drift towards the positive terminal. The speed of this drift is called he drift velocity. What effects drift velocity? • More collisions, more drift velocity • The thickness of the wire affects this • The speed of the electrons affect this • The number of free electrons affects this (drift velocity depends on material) Charge carrier density This is a measure how many free electrons there are in a material per m3. Symbols n = Charge carrier density A = cross sectional area of the wire Q or q or e = charge v = drift velocity Equation I = nAqv

1 Kirchoff's first law

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Metals 1) These conduct electricity 2) They have disassociated electrons that move from ion to ion 3) These electrons move in the conduction band Semi-conductors 1) Very few if any disassociated electrons in conduction band 2) The almost conduct electricity 3) Given energy some electrons jump into conduction band e.g. LDR, thermistor Insulators 1) No free electrons 2) Large amount of energy needed to cause electrons to jump into a conduction bond – often material will breakdown first. Whats the effect of temperature? n

A

q

V

Metal

No significant effect


No change

Decreases Decreases Because atoms vibrate more so there are more collisions

Insulator

No change


No change

0

0

Semiconductors

Increases No significant because effect electrons are given enough energy to jump to the conduction band

No change

Decreases

Increases

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2.2 Electrical potential difference and E.M.F. of a cell EMF: This is a measure of a work done on the electrons per coulomb of charge E W P =Q = Q =I P.D: This is a measure of the work done by the electrons on the components in the circuit per coulomb of charge







E=IVt W =IV  t

2.3 Current – Potential difference graphs Ohmic components follow ohms law, resistance is proportional to voltage, graph 1 Tungsten filament lamps, as current increase, voltage increases but as current increases temperature also increases this increases resistance. Graph 2 Semiconductor diode, the diode allows current to flow freely in one direction only. The current increase with voltage, but the rate of increases increases after the voltage has passed a certain point. Graph 3 Thermistor, as voltage and current increase, temperature increases increasing the number of charge carriers, decreasing resistance. Graph 4 2.4 Resistance and resistivity Resistance The opposition to the movement of charge in a circuit – Collisions between charge carriers and ions mostly but also other charge carriers – Temperature increases the number of collisions (ions vibrate more) – Thickness decreases resistance because if a wires is thicker then more electrons can travel at the same time and there is a lower chance of a collision due to increased number of path – Lengths increases resistance because there are more collisions The resistivity is a property of that material, it has the same value no matter what dimensions the material has. L R= A Power Dissipation  ⇒ resistivity  m V2 L⇒ length P= IV =I 2 R= A⇒ cross sectional area R 1 = () conductivity Anthony Cameron


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Electrical circuits 2.5 Conservation of energy Around any closed loop, the sum of the e.m.f.s is equal to the sum of the p.d.s2

=  p.d. Internal resistance Internal resistance: All power sources in a circuit have internal resistance. Hence p.d. Across a battery is less than e.m.f. when a current flows.



V = −IR

therefore

=V IR 

When the battery is disconnected from the circuit I =0 therefore =V When the cell is connected across a component then the voltage will reduce because of its internal resistance On an IV graph: EMF = V + IR y=V V = EMF – IR M = -R- The internal resistance of the cell x=I c = EMF 2.6 Series and parallel circuits Resistor in series The total resistance of a number of components in series is simply the sum of the individual resistance so for resistors in series: Rt = R1 + R2 + ... + Rn Resistors in parallel I t= I 1I 2 V Rt = It V V V therefore =  Rt R1 R 2

so for resistors in parallel

1 1 1 1 =  ... Rt R1 R 2 Rn

Adding Cells If a cell is added in series, the total EMF and internal resistance is the sum of the speerate cells EMFs or resistance When two cells are added in parallel, emf and resistance must be calculated using Kirchoffs laws 2.7 Change of resistance with temperature and illumination Thermistors and LDRs are semi-conductors and therefore when provided with electricity, electrons move into the conduction band, the greater the energy the greater the conductivity (less resistivity). 2.8 Potential divider By creating a circuit with two resistors then putting another two circuits, each is in parallel with one of the resistors, the circuit attached to the resistor with the highest value of resistance will have a greater potential differences. This is because V = IR 2 Kirchoff's second law

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Heating matter 2.9 Specific heat capacity (c) E = mcΔt (Specific refers to “per mass”) 2.10 Specific latent heat (l) E = ml Energy released or absorbed by 1 kg of a substance during a phase change P1 V 1 P 2 V 2 F = 2.11 Pressure p= 0oC = 273K A T1 T2 Kinetic model of matter 2.12 & 2.13 Ideal gases An ideal gas – the time for the collision is small relative to the time between collisions, elastic collisions, size of the molecule sis small compared to the volume, molecules move at a constant speed between collisions p1V 1 p2V 2 pV = Therefore =Constant T1 T2 T pV =nR R⇒ molar gas constant T pV =nRT The ideal gas equation In a closed box with volume xyz a molecule travels parallel to face L X at Velocity v x hits side, change in momentum⇒  P  P=mv x −−mv x  =2mv x 2L 2L v x= x t= x t vx 2L x mv x 2 P F= =2mv x ÷ = t vx Lx However there is usually not just one molecule but N moles, 2 2 2 mv mv mv F also there are 3 pairs of faces rather than one and the mean x p= = x = = x A Lx A Lx L y Lz V square speed is 〈 c 2 〉 Nm 〈 c 2 〉 therefore p= 3V 1 pV = Nm 〈c 2 〉 3 Nm V 〈 c 2〉 p= 3

=

1 pV = N m〈c 2 〉 3 1 pV = N ×2KE 3 pV =nRT 1 N ×2KE=nRT 3 3 nRT n R KE= × =N −1 =k A 2 N N NA 3kT KE= 2 Browninan motion Brownian motion states that because the forces on a particle will be unbalanced (this is due to the particles around it) it will move randomly. Anthony Cameron


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Conservation of energy 2.14 & 2.15 Internal energy & Heating For real gases the random distribution of potential and kinetic energy amongst molecules. Appreciation that hot and cold objects have different concentrations of internal energy. internal energy - total kinetic and potential energy of a molecule. Energy will move from a hot body to a cold body and from a old body to a hot body, however a hot body has more energy and therefore more energy moved from it, eventually the energy of the hot and cold body become equal and the movement becomes equal. U = internal energy Mechanical work – transferring energy by adding a force to an object. Increase in internal energy = work done on the block ΔU = ΔW Work done = force x distance W = Fx, for a gas W = ρΔV Electrical work – transferring energy using electrical current Increase in internal energy = energy transferred by working ΔU = ΔW Work done = power x time W = VIt Heating Increase in internal energy = energy transferred by heating ΔU = ΔQ The zeroth law of thermodynamics – If object A is in thermal equilibrium with object B and B is in thermal equilibrium with object C. Then A must be in thermal equilibrium with C. The first law of thermodynamics – Energy is conserved therefore, the increase in internal energy is equal to the energy gained by heating plus the energy gained by working i.e ΔU = ΔQ + ΔW 2.16 The heat engine. This describes the transfer a energy from a hot place to a cold place and the use of this is to do work. Q1 joules of energy are transferred to the water at the boiler, W joule is the work done on the turbine that powers the generator and Q2 is the remaining energy that is transferred to the atmosphere via the cold sink. Q W Q −Q2  Efficiency of a heat engine= = 1 =1− 2 Q1 Q1 Q1 T 1−T 2  T2 Maximum thermal efficiency of a heat engine= =1− T1 T1 The limitation of the efficiency of a heat engine is how cold the cold sink can become and how hot the hot source can become. The heat pump Work needed to pump energy from cold to hot. The energy given to the hot object equals energy taken form the cold plus the work done Ordered and disordered processes • Doing work on a system is an ordered process, the energy transfer travels in one direction only. It is predictable • Heating a system is a disordered process. Quanta of heat travel both ways in an unpredictable way. Anthony Cameron


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Unit 3A: Astrophysics A1 Observing stars Charge coupled devices (CCD) are used to record images of stars. They are efficient, they detect small amounts of light and the output is linear (linear response) that means that the output signal is proportional to the light received. A problem with photographic film is that if the film has a large grain it will be sensitive to light but the image would be clear while a smaller grain film would be less sensitive to light and the image will be sharper. The atmosphere affects the light from stars and thereby hinders observations. Changes in atmospheric density cause stars to twinkle, more than 30% of the visible light is scattered and different wavelengths of light will be received. The Infra red Astronomical Satellite (IRAS), Cosmic Background Explorer (COBE) and the Hubble telescope are satellites used for deep space imaging. Luminosity is the power emitted by the star (measured in watts). L = σT4A Intensity is the power radiated from the star that reaches earth (power per metre squared) Energy Distribution

The energy distribution shows the intensity of various wavelengths of radiation emitted from a given star. Wiens Law λmax x T = 2.898 x 10-3 Where λmax is the wavelength of the radiation with the greatest intensity that is emitted by the star. And T is the surface temperature of the star Surface temperatures of stars range from near absolute zero to 107 K, corresponding to peak wavelengths from radio to X-rays.

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Luminosity=×T 4 ×surface area −8 −2 −4 =Stefans Constant =5.67 x 10 Wm K L Intensity= 2 4 D  max×T =2.898 x 10−3 revision 88 12 of 60

Measuring distance by trigonometric parallax (the angular displacement of an object when viewed from separate points). The stars position is recorded against the static background of more distant stars when the Earth is at opposite extremes of its orbit around the sun. The parallax angle is 1 measured and using trigonometry the distance= . This is assuming that the distance from tan p the earth and the sun at both points is 1 AU. A limitation of this method is that the smallest angle that can be used to get an accurate result is 1/360000 thereby limiting the maximum distance this method is able to measure at 1018m

↑ Trigonometric parallax ← The Hertzsprung-Russel Diagram

1. 1) 2) 3)

Measuring the distance of distant stars Spectrum – determine Temperature from λmax (Wiens Law) Use temperature to determine luminosity (HR diagram) Then use intensity and Luminosity to determine distance

Cepheid variable stars Variable stars undergo variations in luminosity, Cepheid variable stars expand and contract leading to variations in luminosity. The period of the contractions is related to the absolute magnitude of the star and therefore if two stars have the same period their absolute magnitude will be the same and therefore if the magnitude of one of the stars is known then the distance of the other can be calculated.

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A2 The lives of stars Stars – Energy from fusion In the centre of a star a process called the proton-proton chain. This is a process by which the star receives its energy. This process starts when the sun is a cloud, as particles in the cloud become closer together (gravitational collapse) PE decreases and KE increases, T ∝ KE, therefore T increases this starts the process of fusion (burning hydrogen). 1 1 2 0 + (a) 1H 1 H  1H 1 v 2 1 3 (b) 1H 1 H  2 He  3 3 4 1 (c) 2He  2He  2He 2 1H v ⇒ neutrino Summary: 4 protons ⇒ helium nucleus + energy therefore Mass of energy released =Mass of four protons−Mass of helium nucleus and from this E=mc2 Giant molecular cloud (Stellar Nursery), areas with a high density of particles. Areas of higher density have a higher gravity and therefore particles will move towards them. As temperature and pressure increases, the clumps of particles become protostars. As these become hotter, the fusion of hydrogen starts at 10 megakelvin. The star becomes a main sequence star until it expands all of its hydrogen into helium (larger and hotter stars produce helium more quickly) where it moves off the main sequence. Stars less with masses lass than 0.4 of the sun's mass burn hydrogen slowly. They become white dwarf stars Stars between 0.5 and 8 times the mass of our sun become red giants at the end of their lives. When the hydrogen runs out the fusion of hydrogen stops and the sun starts to contract as there is no longer hydrostatic equilibrium. As the sun contracts, temperature increases, this allows the helium to fuse, when the helium runs out the sun contracts again and temperature increases, this allows the carbon to fuse, this process continues until iron is created, this cannot be fused. This process creates layers of elements with iron in the core and hydrogen near the outside, the energy from the fusion expands the outer layers. Matter is lost from these layers as gravitational field is weak. When they have expanded all fuels they contract and GPE decreases and the star becomes a white dwarf. Stars with masses greater than 8 times that of the sun become super giants, when the hydrogen runs out, the sun contracts and the temperature increases causing the helium to fuse, as the fuels run out the star contracts and temperature increases and the elements fuse into something heavier until the star becomes layered with iron3 at the centre and hydrogen on the outside. When the core is iron fusion stops and the star contracts until it becomes energetically favourable for there protons and electrons combine to form neutrons and the core collapses rapidly and a large amount of energy is released blowing away the outer layers into space – type II supernovae, leaving a core remnant. If the core remnant after a supernova is more than 1.4 solar masses the central core of neutrons left behind is more likely to form a neutron star, they are extremely dense and due to low temperature they can not be seen however because they are magnetised and rotating, they continuously emit high frequency radio signal along their magnetic axis. Hence the name pulsar. If core remnant is greater than 2.5 solar masses it will contract until it becomes a singularity, a black hole, anything that passes the event horizon, can never build up enough velocity to escape. 3

as this cannot produce energy by fusion due to the high amount of energy required for fusion

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Summary of star classes White dwarfs. Hot, low volume, low mass stars. Origins and typical masses, (less than about 1.4 solar masses). Core remnants. Red giants. Cool, high volume, stars. Origins and typical masses, (between 0.4 and 8 solar masses). Core remnants. Supernovae (Type II only). Rapid implosion of stars of more than eight solar masses. Shock wave: outer layers blown away. Neutron stars. Core remnants greater than about 1.4 solar masses. Formation from electrons and protons. Very high density. Pulsars. Black holes. Core remnants greater than about 2.5 solar masses. The dense core traps radiation.

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Unit 4: Waves and our universe Circular motion and oscillations 4.1 Angular Speed, Period and Frequency

&

4.2 Acceleration and resultant force

Following a circular path at a constant velocity is called 'uniform circular motion' Angular speed (ω) is the magnitude of the vector quantity angular velocity, it is the proportion of a complete circle per second. The period (T) of a body doing uniform circular motion is the time it takes to complete one revolution. The frequency of rotation is the number of rotations per second. Distance=2  r  2 = = =2  f v =r Time=T t T linear velocity=v 2 r Average speed=v= v2 angular velocity= T a= =r  2 r 4 2 r Average acceleration= 2 mv2 T therefore F= r mv 2 =the centripetal force=the sum of all forces acting on an object r mv2 e.g. =mg−R r F=

When in free-fall, none of the supportive upward forces are present and as such there is only downward acceleration of g and so the body feels weightless. As a shuttle descends at an acceleration almost equal to g the occupants will be falling at the same acceleration and as such they will not move but be suspended. Velocity is a tangent to the circle, however the change in velocity and therefore the acceleration and force is directed towards the centre of the circle. The centripetal force is the external force required to make a body follow a circular path at constant speed. The force is directed inward, toward the centre of the circle. 4.3 & 4.4 SHM Simple harmonic motion A harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x according to Hooke's law: F = -k x Simple harmonic motion is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. SHM – A periodic motion of constant frequency where the acceleration is always directed towards the centre of the oscillation. The motion is sinusoidal in character and as such the displacement-time, velocity-time and acceleration-time graphs will all resemble sine/cosine waves. The graphs have a phase difference of ½π from the previous. This is because when displacement is greatest velocity will be zero and acceleration will be at its lowest. ma=−kx 2 F =−kx a=− 2 x T= k  x compare with a=−2 x ⇒ a=− m 2 k k 2 by substituting =2  f a=−2  f  x = = m m





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SHM – Acceleration is proportional to displacement and directed towards the equilibrium position

4.5 Undamped simple harmonic oscillations x0 = |maximum displacement| x =x 0 cos t  dx v = =− x 0 sin t as such the maximum speed is 2 f x 0 dt dv a= =−2 x 0 cos t dt 4.6

Mechanical oscillators, pendulums and springs

 

k m k is the spring stiffness m T =2 k =



For small-angle swings, the period of a pendulum length of l is given by: T =2



l g

4.7 Resonance When you give a small displacement to a system it can oscillate, it oscillates at its own frequency. This is the oscillator's natural frequency. If energy is being removed from the system, so the oscillations are becoming smaller and smaller, we say that the oscillations are being damped. The higher the damping the faster the oscillations will reduce in size. Critical damping is the damping required to make the oscillations stop in the quickest possible time without going past the equilibrium position. Resonance is the tendency of a system to oscillate at maximum amplitude at a certain frequency. This frequency is known as the system's resonance frequency, when damping is small, the resonance frequency is approximately equal to the natural frequency of the system. When the driving frequency is equal to the natural frequency of the driven system, large-amplitude, even violent, oscillations may result. This effect is called resonance. Resonance occurs when the driving frequency is equal to the natural frequency of the system you are driving. The energy of an oscillating object is constant, as when the velocity (which KE is proportional to) is greatest, potential energy is smallest. This potential energy changes as displacement of the object from the ground and the potential energy in the spring changes.

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Waves 4.8 Mechanical waves on water, along springs and in air (sound) A wave is a means of transferring energy from one point to another without there being any transfer of matter between the points. A wave can either be mechanical or electromagnetic and a wave can either be longitudinal or transverse. A mechanical wave travels between two points through a medium. 4.9 Electromagnetic waves Electromagnetic waves are transverse waves, they oscillate perpendicular to the direction they travel. E.M. Waves with differing frequencies have different properties.

The electromagnetic spectrum Type

Wavelength

Long-wave radio

~ 1200 m

Medium-wave radio ~ 300 m

Generation

Uses

Oscillating current in aerials

Radio

Short-wave radio

~ 30 m

VHF

~3m

UHF

~1m

Microwaves

~ 10 cm

Directly produced in waveguides

Radar, cooking, communicating

Infra-red

~ 1 μm

Hot bodies, LEDs

Night-sights, heating, shortdistance communication

Visible Light

700 – 400 nm Very hot bodies, LEDs

Ultra-violet

< 400 nm

Extremely hot bodies, sparks, discharge tubes

Sun-tanning, detecting invisible marking, sterilisation

X-rays

~ 10-10 m

Stopping fast electrons

X-raying people and materials

Nuclear decay

X-raying thick objects, killing cancerous cells, sterilising

-12

Television

Gamma rays

~ 10

Cosmic rays

Very short

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m

From distant parts of the universe


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4.14 & 4.10 Stationary and progressive waves Waves that travel out from a source and that carry energy are called travelling or progressive waves. Stationary waves are called standing waves. These do not transmit energy. These are caused by the superposition of 2 waves of the same frequency etcetera, propagating in opposite directions. They do not move.

Compressions and Rarefactions of a "Longitudinal Waves" Longitudinal waves, the oscillations of the particles is parallel to the direction of travel. Composed of compressions and rarefactions. Transverse waves, the oscillations of the particles is perpendicular to the direction of travel.

Plane polarisation. With longitudinal waves if the plane is rotated around the direction of the wave, the particles will still be oscillating in the same direction. However as transverse waves oscillate perpendicular to direction to travel, rotation will cause a the particles to oscillate in other directions which are still perpendicular to the direction of the wave. Longitudinal waves which are only oscillating in one direction are considered plane polarised. Unpolarised light waves can be polarised using grilles, if two grilles are placed in front of each other and one is rotated light will be blocked out completely.

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4.11 Conservation of energy for waves in free space from a point source Inverse square law. As a wave spreads out it gets weaker the further it becomes from the source. Its power is spread over a larger area, so the power per unit area is diminished. The power per unit area is called the P P energy flux (ɸ) or intensity (I) therefore ɸ ∝ D-2. =I = = 2 2 4r 4 D This relationship of energy flux to the inverse of distance squared is called the inverse square law. Superposition of waves 4.12 Superposition of waves Superposition When two waves meet each other When two waves meet and enhance each others amplitude, this is constructive interference. When two waves meet each other reducing there amplitudes this is destructive interference. When waves meet in phase constructive interference occurs When waves meet completely out of phase destructive interference occurs Sine and cosine wave are both sinusoidal Phase - The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 Path difference – is the difference in the distance travelled, At the point where two waves meet the difference in the distance they have travelled is the path difference

The path difference here is the difference between two peaks. When two waves of the same frequency meet with a path difference i) nλ – constructive interference occurs ii) (n + ½)λ – destructive interference occurs From two sources, when the path difference is an integer of λ, constructive interference occurs When the path difference is ½λ, destructive interference occurs The wavefront is the locus of points with the same phase. Path difference Phase difference = Wavelength 2 Diffraction: The spreading out of a wave as it passes through an aperture. Smaller aperture and larger wavelength leads to more spreading out There will be no diffraction if the wavelength is many times larger than the aperture

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A2 Physics notes Compiled by Anthony Cameron 4.15 4.16 Coherent Monochromatic

Diffraction at a slit → Coherence & Two slit interference patterns – Same phase – A wave of one frequency

Young's 2 slit experiment

Sunlight is passed through a screen with a single slit and a filter to give it coherency and monochrome. The coherent wavefront of light impacting on the twin slits is divided into two new wavefronts that are perfectly in phase with each other. Light waves from each of the slits must travel an equal distance to reach point A on the screen illustrated in Figure 1, and should reach that point still in phase or with the same phase distance. The two waves reaching point A are in phase and therefore constructive interference occurs, producing a bright red interference fringe on the screen. Where destructive interference occurs dark regions appear on the screen. This causes a fringe. For light, fringe separation is very short. It is difficult to measure path differences very accurately. x  = D s =wavelength m 400−700nm x=fring seperation m a few mm s=slit seperation 0.5−1.5mm D=distance from slits to screen 1−10m The difference between the distances between the two sources and the maxima is called the path difference. At the first maxima from the central maxima the path difference equals the wavelength and at the second maxima the path difference equals twice the wavelength Anthony Cameron


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Quantum phenomena 4.17 The photon model of electromagnetic radiation Radiation is emitted in small discrete packet called quantum (pl. quanta), a quantum of electromagnetic radiation is a photon. The energy of these quanta is proportional to the frequency of the photons. E = hf were h is plank's constant (6.626 x 10-34) The photoelectric effect. The Work function and the photoelectric equation. Photoelectric effect – electrons are emitted from a metal surface when exposed to light, this is because when a photon hits an electron either the photon will be reflected or the energy would be absorbed transferring all its energy to the electron. If the latter happens then an electron will be promoted depending on the energy of the photon, if the photon has enough energy the electron will be released. The minimum frequency required for a photoelectron to be released is the threshold frequency Properties ● Emission is instantaneous (If light was completely a wave the energy would be spread along the wavefront and no electron would instantly receive the energy required to escape from the surface) ● Emission only occurs if the frequency is above the threshold frequency f0 ● The number of electrons emitted is proportional to the brightness of the light ● Electrons have varying Ek – up to a maximum which depends on the frequency of the radiation ● The Ek of the electrons is independent of the brightness of the light ● Red light will not cause the emission of electrons ● A weak violet light will emit only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths The work function, ϕ is the minimum energy a photon requires, to remove electrons from the surface of the metal. Φ = hf0 Φ, Minimum photon energy required, for photoelectron emission from the surface of the metal

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Photoelectric emission experiments This photoelectric can be seen using a gold leaf electroscope. If a zinc plate is cleaned of its oxide layer, placed on top of the electroscope and negatively charged. The excess electrons repel each other and move to the top and bottom of the stem of the electroscope. If the plate is subjected to photons from light (UV), electrons will be repelled reducing the overall charge and causing the leaf to slowly fall down. The Kinetic Energy (Ek) of the electrons can be up to {hf – ϕ}, the photon energy minus the work function. Most will have less than this as they lose energy in collisions as they exit the surface. As such KEmax = hf – ϕ. The graph is shown below ↓

To measure the energy of a photoelectron a photoemmisive cell, shown below, is used. When light hits the photoemissive cathode electrons are released across the vaccum into the wire anode and the picoammeter indicates a current.

Effect of increasing voltage As the voltage is increased, the current will increase as more electrons are attracted to the anode, until the saturation current is reached. The saturation point is when all the photoelectrons reach the anode. A greater intensity will increase the saturation current. Negative voltage When the voltage becomes negative it repels the electrons and at a certain negative voltage, called the stopping potential (Vs). the current will be reduced to zero as all the electrons are repelled by the other. The stopping potential depends on the energy of the photoelectrons so KEmax = eVs and therefore qVs = hf – ϕ Hence a a greater amount of EM energy will result in a greater stopping voltage

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4.18 Energy levels An atom has a fixed energy corresponding to the orbital in which its electrons move around the nucleus. The atom can accept a quantum of energy to become an excited atom, if that The electrons orbiting a nucleus can be found at different energy levels. It is possible to excite electrons into higher energy by shining specific frequencies of light. Each element has its own unique pattern of energy levels and frequencies that cause excitation. When an electron becomes free the potential energy will be zero, however as the electron moves away its potential energy increases, hence the energy levels have minus values. The energy delivered to the electrons is equal to the energy difference between the levels hf = E1 – E2 Shortly after becoming excited the electrons will drop down to a lower state. Doing so the lose energy as a photon. The frequency of the light emitted can be calculated using: hf = E1 – E2 Electrons can exist at any of these energy levels, to move from one level to another energy is required To excite from ground state to the first excited level requires -3.4 - (-13.6) = 10.2 eV as hf = E2 – E1, the above transition can occur when a photon of the right frequency is absorbed by the electron. hf = 10.2 x 1.6 x 10-19 1eV = 1.6 x 10-19J -19 -34 f = 10.2 x 1.6 x 10 / 6.63 / 10 = 2.46 x 1015 Hz Release – energy level goes down Absorption – opposite

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4.19 Wave properties of electrons & Wave particle duality Diffraction is a property of waves, when a laser is shone through a diffraction grating: ↓ When a laser is shone through two diffraction gratings at a right angle to each other: ↓ When the laser is shone through many diffraction gratings at many angles↓ This shows the diffraction of light many times will lead to concentric circles. Electrons being particles and not waves should not do this but when a electrons are fired through a thin piece of graphite (the thin graphite crystals act as the multitude of diffraction gratings at different angles) concentric circles form.

This can also be seen when performing the double slit experiment with electrons, slowly an interference pattern builds up. → DeBroglie suggested that electrons had wave properties and therefore they had a wavelength inversely proportional to the particles momentum. h deBroglie wavelength== p The rings and the interference pattern build up because the electron is diffracted, this happens because the de broglie wavelength is similar to the slit spacing. s ≈ λ To explain the photoelectric effect, waves must be able to act Each dot is where an electron hit, slowly an interference pattern builds up like particles as the emission of a photo electron is instantaneous. If light was completely a wave the energy would be spread along the wavefront and no electron would instantly receive the energy required to escape from the surface. Wave-particle duality is the concept that waves carrying energy may have a corpuscular aspect and that particles may have a wave aspect. For example to explain the photoelectric effect, e.m. waves must act as particles, while electrons need to be thought of as de Broglie waves in electron diffraction If the electron in hydrogen is modelled as a particle orbiting the proton then it Apparatus for the double-slit should radiate energy and spiral towards the proton. It does not because of its experiment with electrons wave characteristics, each allowed orbit corresponds to a standing wave with all the energy in the wave. There are a complete number of waves in each orbit . The wave describes the probability of an electron's location More waves in higher orbit – higher frequency – higher energy. Discrete energy levels corresponding to successive standing wave patterns ↑ Stationary waves in the hydrogen atom Wave properties of electrons in atoms Anthony Cameron


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The expanding universe 4.20 Optical line spectra The emission spectrum of a body or substance is the characteristic range of radiations it emits when it is heated, bombarded by electrons or ions, or absorbs photons. As each atom emits a unique set of frequencies, this method can be used to find chemical composition. The absorption spectrum is produced by examining, through the substance and through a spectroscope, a continuous spectrum of radiation. The energies removed from the continuous spectrum by the absorbing medium show up as black lines or bands. With a substance capable of emitting a spectrum, these are in exactly the same positions in the spectrum as some of the lines and bands in the emission spectrum. 4.21 Electromagnetic Doppler shift. “The Doppler effect is the change in frequency and wavelength of a wave as perceived by an observer moving relative to the source of the waves.” If an object is moving away at a greater velocity from the observer than the wavelength of light emitted behind it will lengthen. If an object is closing on the observer than the wavelength of light will shorten. The lengthening of the wavelength is known as red shift and the opposite blue shift as this is to which ends of the EM spectrum the frequencies of light will shift to. Light year=c×365.25×24×60×60 m  f  v = = f  c A light year is the distance light travels in a year By measuring the red shift of receding galaxies, astronomers determined distant galaxies are receding faster than closer galaxies. Hubble plotted the distance of galaxies against their recession velocity and found a correlation. So v = HoD where H0 (or just H) is Hubble's constant. H0 ≈ (2 ± 1) x 10-18 s-1

Uncertainty in d and H

Explanation of the universe, Hubble's law & the big bang The Big Bang is the cosmological model of the universe whose primary assertion is that the universe has expanded into its current state from a primordial condition of enormous density and temperature. Assuming all galaxies started at the same point in space, the age of the universe can be worked out as D D Age= = =H −1 v HD There are three major possibilities for the end of the universe. These all depend on the average mass-energy density of the universe and the critical density of the universe which is precisely the value required to halt the expansion of the universe. If the average mass density of the universe is greater than the critical density, the universe is closed, expansion will slow down and the universe will then start contracting, collapsing back on a single point, the big crunch. If it is less than the critical density than the universe is open and the universe will continue expanding but at a decreasing rate. If it equals the critical density then the universe will expand at a lower rate than the open universe theory, however eventually all motion of galaxies will cease. Anthony Cameron


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Graph showing fate of the universe – there are two possibilities indefinite expansion or final contraction Ω < 1 Closed universe Ω = 1 Critical density Ω > 1 Open universe

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Unit 5: Fields and forces Gravitational fields 5.1 The concept of a field A field is a region in which a force acts. The lines in the diagram to the right are field lines, they represent the gravitational force of the earth. The relative density of the arrows represents the relative strength of the field, the arrow represents the direction of the force. In this case the arrows point towards the Earth's centre of mass as this is the direction of the force any object will feel in this field. Closer to the surface these lines are virtually parallel and equidistant, as such close to the surface of the Earth, the Earth's gravitational field can be considered in this small region, to be uniform → Gravitational field strength. The region in which a body exerts the force of gravity is a gravitational field The gravitational field strength (referred to as g) at a point in a gravitational field is the force per unit mass exerted acting on a mass placed at that point Gravitational field strength is a vector quantity. Its direction is that in which a mass would move under influence of the field For an object in free-fall; a = g 5.2 Force between point masses Gravitational forces are the result of mutual attraction between two objects. They occur between all pairs of objects. Newton's law of gravitation, force of gravity between two objects is proportional to the product of their masses and is inversely proportional to their distance. So Newton's law of gravitation Gm1 m2 states where G, the universal gravitational constant equals 6.67 x 10-11 Nm2kg-2 F= 2 r With spherical objects r is the distance between there centres or mass Gravitational field strength in radial fields. F GM The gravitation field strength equals g = = 2 , where m is the mass of the attracted object, m r and M is the mass of the attracting object. Equipotential surfaces. (The relationship V = – Gm/r is not required.) Equipotentials join points of equal potential. As such all points in a field which have the same potential can be imagined as lying on a surface (an equipotential surface), or a line if 2 dimensional, moving objects from one point to another on this surface requires no energy. Equipotentials are always perpendicular to field lines. This allows satellites to orbit with no energy required. For stable orbiting objects the centripetal force is the gravitational force Kepler's first law of planetary motion: The shape of a planetary orbit is an ellipse with the Sun at one of the foci Kepler's second law of planetary motion: A line (radius vector) joining a planet and the sun sweeps out equal areas during equal intervals of time. Kepler's third law of planetary motion: The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits. P2 ∝ a3 Anthony Cameron


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g=

F m

Electric fields 5.3 Electrostatic phenomena and electric charge Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields. Electric charge is either positive or negative, like charges attract and opposite charges repel, charge is discrete (it is always a multiple of e, the elementary/electronic charge (1.6 x 10–19 C) and charge is always conserved. The unit of charge is a coulomb. The coulomb is the quantity of charge which passes any section of a conductor in one second when a current of one ampere is flowing, i.e. 1C = 1As 5.4 Electrical lines of force Field lines (lines of force) represent electric fields in diagrams. The arrows show the direction of force on a small positive charge. And the density of the arrows shows the relative strength of the field

Electric field strength Electric field strength (E) at a point is the force exerted by an electric field on one coulomb. The unit of electric field strength is NC–1.

E=

F Q

5.5 Force between point charges The force between two point charges is proportional to the product of the two charges and is inversely proportional to the distance between the charges squared. Hence F= kQ 1 Q 2 and in vacuum or air k = 9.0 x 109 otherwise k = 1 Where ε is the 4 0 r2 permittivity of space.

5.6

E=

F kQq 1 kq = 2 × = 2 Q Q r r

Electric field strength in radial fields

F V F Electric field strength in uniform fields E=QV =Fx E= = Q Q x The potential difference between two points in an electric field is numerically equal to the work done in moving a unit positive charge from the point at the lower potential to that at the higher potential. W = QV 5.7

E=

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Electron beams Electron beams are emitted from electron guns, the most common sort emits electrons through thermionic emission. A heats a cathode which emits electrons which are attracted to the anode, some will be forced through the hole. The potential energy lost moving from the cathode to the anode is equal to the kinetic energy gained and as such the kinetic energy of the electron equals the product of the electrons charge and the potential difference between the two electrodes. 1 2  m e v =e V 2

Capacitance 5.8 Capacitance Capacitance is the measure of how much charge can be stored at a particular voltage and is equal to the charge required to cause unit change in the potential of a conductor. Q C= the unit of capacitance is the Farad (F) V

The charging of a capacitor, the arrow represents the direction A capacitor consists of two parallel plates, when a potential difference is applied across of electron flow

the plates there will be a momentary flow of current. Electrons are drawn from plate A by the battery's positive terminal and electrons are deposited on plate B by the action of the negative terminal. Hence plate A becomes positively charged and plate B becomes negatively charged. When the potential difference across the capacitor equals the potential difference across the battery, the capacitor is 'fully charged'. The charge on plates A and B are equal and opposite. 5.9 Capacitors in series and parallel circuits Capacitors in series Capacitors in parallel For components in series, voltage will be the sum For components in parallel, voltage will be the of all the component voltages, and current (and same for each capacitor and the total sum of their therefore charge) will remain constant. currents will be the sum of all the component Q currents V t =V 1V 2...V n Substitute V = I t =I 1I 2...I n Substitute Q=It=VC C VC t VC 1 VC 2 VC Q Q Q Q =  ... Q cancels out =  ... n C t C1 C2 Cn t t t t 1 1 1 1 V and t cancel out leaving; =  ... C t =C 1C 2...C n C t C1 C 2 Cn Comparison with resistance Capacitance across series and parallel follows an opposite rule to that of resistance. This is because Resistance is proportional to voltage but capacitance is inversely proportional to voltage i.e.

V =IR=

Q C

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V ∝ R∝

1 C


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Graphs for a capacitor charging

Charge against time

Current against time

Graphs for a capacitor discharging

Charge against time

5.10

Current against time

Energy stored in a charged capacitor.

Q ⇒V ∝Q C Hence if a graph of potential difference against charge of a capacitor is graphed, the resulting will line will be straight. As E = QV, the area under this graph will be the energy stored in the capacitor. This area under the graph is triangular and so is equal to ½QV so; 1 E= QV and by substituting in Q=VC 2 V 2C Q2 E= = 2 2C V=

This can also be shown using calculus, as the work done transferring charge from one plate to another is the product of the potential difference between the two plates and the size of the charge being transferring so; Q  W=V  Q=  Q hence; C Q Q Q Q2 Q2 W =∫ dQ = = 2C 0 2C 0 C

[ ]

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Magnetic fields 5.11 Permanent magnets The region surrounding a magnet in which magnetic effects can be experienced is the magnetic field of the magnetic. The direction of this field is the direction in which a north magnetic pole would move under the influence of the field if it was placed at that point. The path which such a pole would follow is called a magnetic field line. Opposite poles attract, while like poles repel. A Neutral point is a point where overlapping magnetic fields cancel so the resultant field strength is zero. An example of a neutral point The denser the magnetic field lines the would be the area directly between two repelling magnetics. stronger the magnetic field. The magnetic field lines go from the north to the south pole of the magnet ← Field lines for magnets attracting and repelling each other, the neutral point is directly between the two north poles in the first diagram

Fleming's left hand rule → describes the direction of thrust on a conductor carrying a current in a magnetic field. 5.12 Magnetic flux density (B-field) B is the symbol that represents Magnetic flux density, this is the force acting per unit current length. The unit of B is the Tesla (T). B is a vector, the direction of B is that of a tangent to the field line at that point but can also be found if the left hand rule is applied. If the field lines are parallel, the field is uniform so magnetic flux density is constant. Magnetic flux density is not the strength of the magnetic field but the ability of the field to apply a force F on a wire length L with a current of I flowing through it hence; F = BIL

Simple Differences between Electric and Magnetic fields Electric field – E

Magnetic field – B

Can be due to single charges

Cannot be due to single poles

Acts on moving and stationary charges

Only acts on moving charges

Produces force parallel to field

Produces force perpendicular to field

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5.13 Magnetic effects of a steady current Wires will have a circular magnetic field round them, the direction of the field depends on the direction of the current. If wires are coiled the fields combine and become directed through the centre of the coil. This coil is called a solenoid and has a magnetic field as shown below, the magnetic flux densities are constant throughout the centre of the solenoid as the field there is uniform.

If the thumb represents the current, the curled fingers of the right hand represents the direction of the field

Hall effect When a magnetic field is applied perpendicular to a conductor through which a current is flowing, there will be an increase in potential difference on the opposite sides of the conductor. This happens because the charge carriers will experience a force when a magnetic field is applied perpendicular to the direction of current. This causes the charge carriers to change direction and collect on one side. The surplus on one side and the deficit on the opposite side, hence more charge carriers are attracted to one side. This an be used to measure magnetic flux density, by taking a semiconductor passing a current through it and connecting it to a sensitive voltmeter. This is a Hall probe. As the Hall voltage is proportional to the magnetic flux density, the Hall probe can be used to determine magnetic flux densities The hall effect Flux density due to an infinitely long straight wire Flux density on the axis of an infinitely long solenoid  I B= 0 B= 0nI 2r μ0 is the permeability of free space, r is the distance from the wire, n is the turn density (number of coil turns per unit length) and I is the current flowing through the wire

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Electromagnetic induction 5.14 Magnetic flux, flux linkage Magnetic flux (Φ) is a measure of quantity of magnetism taking into account strength and extent of the magnetic field. The unit of magnetic flux is the Weber (Wb) 1 T = 1Wb m–2 Flux linkage (λ) is the product of the number of turns of a coil and the magnetic flux through the coil. 5.15 Electromagnetic induction By passing a magnet through a coil of wire an EMF can be induced. As the free electrons in the conductor are moved by the magnetic field. Faraday's law. The magnitude of the induced EMF in a circuit is directly proportional to the rate of change of flux linkage or to the rate of change of cutting of magnetic flux. Lenz's law. The direction of the induced e.m.f. is such that it tends to to oppose the flux change causing it, and does oppose it if induced current flows. These two laws can be summarised as;

=− dtd  N  Lenz's law is an example of the principle conservation of energy. As when a magnet is pushed towards the coil there is resistance, hence energy is required to push the magnet forward and when the magnet is removed from the field there is resistance to that so more energy is required to keep the magnet moving. With induction involving a straight conductor, the direction of motion is opposite to the motion of a conductor caused by a current flowing in the same direction a magnetic field in the same direction, hence a right hand rule can be applied for a straight conductor inducing an EMF by passing through a magnetic field. EMF of a straight conductor, lengthl , moving through an uniform magnetic field with velocity v d =−N N is constant so dt dA =−N B =BA and B is constant dt

 

=−Blv

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F=B I l =BA =N 

5.16 The transformer A transformer is used to either step-up (increase) or step-down (decrease) a voltage. It is essentially two solenoids wound around the same soft iron core so they are connected magnetically but not electrically. The side with the input voltage is called the primary coil and the output is called the secondary. The ratio between the two voltages is equal to the ratio of the number of turns on the primary to the number of turns on the secondary, i.e V p N p = Vs Ns The transformer works using the principle of mutual induction, if two coils are close together, then changing the current in the primary coil sets up a changing magnetic field at the secondary coil hence an EMF is induced in the second. Hence a transformer will only work with AC. EMF induced proportional to the rate of change of flux linkage, however the number of primary and secondary coils are constant so. d d So  p=N p and  s=N s dt dt d The core ensures that the flux associated with one coil also passes through the other. As dt remains constant, the equations can be equated as  p  s which becomes  p N p or V Np p = = = N p Ns s N s Vs Ns Eddy currents Any metal moving in a magnetic field or exposed to a changing one, will have EMFs induced in it. This can cause circulating currents, called eddy currents, to flow inside the metal. They will follow low resistance paths so they may be quite large. There magnetic fields will oppose the field which created them, this will slow down a moving body (useful in gauges and other devices with needles which may require electromagnetic damping) and through this and Joule heating energy can be lost.

A common design of transformer

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Unit 6: Synthesis Analogies in physics 6.1 Comparison of springs and capacitors Both capacitors and springs store energy, one is electrical in nature, the other mechanical. With a capacitor the energy comes from a voltage displacing charge from one plate to another, with the spring it is from the force that is extending the spring. V ∝ Q and F ∝ x hence V=Q/C and F = kx  W =V  Q=

Q Q C

hence;

 W =F  x=kx  x x

hence; x

[ ]

kx 2 Wd =∫ kx dx = 2 0

1 = Fx Q Q Q Wd =∫ dQ = = 2 0 2C 0 2C 0 C Similarity; Energy stored in a capacitor equals ½VQ and energy stored in a capacitor equals ½Fx 2 Q

Q

6.2

[ ]

2

Comparison of electric and gravitational fields Gravitational fields

Affects all masses F = mg

Electric fields

Affects all charges

Unit is N Kg-1

F = QE

Unit is N C-1

Obeys an inverse square law Point masses/charges produce a radial gravitational/electrical field Near to the surface of a spherical body, there is an uniform gravitational/electrical field All masses attract each other

Charges can attract or repel

There is no shielding from gravity

Charges can be shielded (Faraday cage)

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6.3 Comparison of capacitor discharge and radioactive decay Over time the energy in a capacitor will discharge, like radioactive decay, capacitor discharge is exponential. i.e. the rate of decay is proportional to the quantity that is subject to exponential decay. dQ Q dN This can be written as: dt =− N for radioactive decay or dt =− RC for capacitor discharge. As such both processes can be graphed as either

−t

N =N 0 e

−

t RC

, where N0/I0 is the I =I 0 e starting number of nuclei/ starting current. With this equation Current is interchangeable with charge, so Q=Q e 0

−

or

t RC

As both processes are subject to exponential decay, theoretically they both go on indefinitely, however as both charge and size of an atom's nuclei have to be discrete values, this is not the case. Both equations can be arranged in similar ways to find t½ (half life), except they will have difference time constants, for radioactive decay is subject to the time constant of λ-1 and capacitor discharge is subject to RC (the product of capacitance and resistance)

N =N 0 e − t ln N =ln N 0− t N ln 0 =ln N 0−t 1 2 2 t 1 =ln 2 2

t 1= 2

ln 2 0.69 ≈  

ln 2 So for radioactive decay t 1 = & for capacitor discharge t 1 =RC ln 2 2  2

Capacitor discharge Radioactive decay I=

dQ Q = dt RC −

Q=Q 0 e

Activity=

t RC

− t

N =N 0 e

Time constant; RC, t 1 =ln 2 RC 2

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dN =− N dt

Time constant; λ–1 ln 2 t 1=  2


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Note dQ =I dt

Accelerators 6.4 Conservation of mass energy Einstein proposed that mass and energy where equivalent, and therefore if the energy of a body changes by the amount E, the mass will change by the amount m ΔE = c2 Δm When dealing with small masses in nuclear physics, the mass can be measured in unified atomic mass units, 1u is one twelfth the mass of the carbon-12 atom. 1u ≈ 1.66 x 10–27 kg 1 u= Nuclear Fission Nuclear fission is the process of splitting a nucleus into smaller nuclei. This is done by bombarding certain heavy nuclei with neutrons causing them to fragment. Fission of certain heavy elements will also produce more neutrons. So essentially each fission event can generate more neutrons each of which can start a new event. These chain reactions can be harnessed and controlled. An element that can sustain a fission chain reaction is called a fissile. An example of which is uranium 235 Fission of heavy elements is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments.

1 kg 1000 N A

Nuclear Fusion Fusion is the union of light nuclei into heavier nuclei. This process will lead to a transfer of mass and consequent liberation of energy. Fusion reactions require energy to start but usually the energy produced is more than enough to propagate the reaction. 6.5 Principles of Linear accelerators To produce charged particles with a large acceleration, it is feasible to use a Van de Graff generator to generate beam of protons each with energy in the order if MeV (Mega Electron Volts). A linear particle accelerator (a Linac) is a device in which charged particles are passed through an evacuated tube with a series of charged plates. The plates are connecting to an AC power supply so that there charge changes. A linac can acceleration particles so they have GeV's of energy. PrincipleAs of linear accelerator a particle can not

go faster than the speed of light, electrons with extremely high energy will have anp.d.s increased mass theelectrons closer there speed gets to the speed of light. Switching to keep accelerating alternating high frequency p.d.

at one instant

–

–

+

+

–

– +

–

+ bunches of electrons between electrodes are accelerated a little later

zero p.d.

bunches of electrons drift through tube a little later still

+

–

+

Anthony Cameron bunches of electrons between electrodes are further accelerated

–

+


+ –

+

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electrodes must be longer because electrons are going faster

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6.6 Principles of Ring accelerators A force acting on a current flowing at 90O to a magnetic field is given by F = BIl The current is given by I = nAQυ So F = B(nAQυ)l. As nAl equals the number of charged particles F = BQυ equals the force on each particle

F = BQv

Placing an electron gun in a glass tube filled with gas, will show the electrons' path as due to inelastic collisions between gas particles and electrons, photons will be released. By then placing this tube near a permanent magnet, a force is produced on the electrons perpendicular to their motion. This causes circular motion. Cyclotron An electric field is used to accelerate a charged particles across a gap between two "D-shaped" magnetic field regions. The magnetic field accelerates the particles in a semicircle, during which time the electric field is reversed in polarity to accelerate the charge particle again as it moves across the gap in the opposite direction. In this way a moderate electric field can accelerate charges to a high energy. This overcame the difficulty of electric discharge caused by the high DC voltages in the Cockroft-Walton and van de Graaf accelerators. Bq =

mv2 r

Bq v = = m r Bq  f= = 2 2 m Colliding beam experiments Theoretically if two beams with equal and opposite momentum collide, they will have zero kinetic energy and momentum. All the remaining energy is used to create new particles.

6.6 Principles of detecting particles Principles of spark and drift chambers A spark chamber is a sealed box with layers of stacked metal plates. High pressure gas fills the space between the plates. A potential difference is applied across alternate layers. As a charged particle moves through the detector, it will ionise gas particles and a spark will be produced.. A drift chamber (sometimes known as a wire chamber) is a detector

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Principle of cloud and bubble chambers Cloud chambers Cloud chambers can be used to track ionised particles that pass through them, essentially they consist of a sealed environment usually containing cooled, supersaturated ethanol vapour. The temperature is maintained by dry ice and the air is kept saturated by felt pads soaked in ethanol. Areas of the vapour will become ionised by the ionising radiation. These ions will act as a condensation nuclei causing nearby ethanol droplets to coalesce and condense forming a mist (this is very similar to the way in which water coalesces with atmospheric dirt to form fog). A light is shined through the tank to show the track made.

Bubble chambers A bubble chamber is filled with liquid gas (usually liquid hydrogen), the pressure is then decreased, so the liquid enters a “superheated metastable phase”, i.e. the liquid gas will stay in liquid form, even though this is energetically unstable. Charged particles travelling through this liquid will ionise causing liquid to vaporise, this causes “bubbles” along the particles track. The chamber is placed in a magnetic field which cause the particles to follow a helical course. Cameras are mounted all around the chamber to produce 3d images, of the microscopic track.

Bubble chamber

Detecting neutral particles This can be done by deduction. You can tell a neutral particle exists by the gap in particle tracks. p → n + β + + υe this equation wouldn't add up without the neutron, so if you start with proton and detect a positron and neutrino you can deduce the existence of a neutron. Anthony Cameron


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Interpretation of particle tracks from a cloud chamber Because of their larger size, α particles will have shorter tracks than β particles, but they will be thicker because of the greater ionising property

From left to right i. The tracks left by alpha particles ii. The single track was left by a highly energetic electron, the squiggly lines are tracks of electrons knocked from atoms by X-rays from the same source as the β particles iii. e.m. radiation such as the X-rays used in this photograph is absorbed by the surface of the cloud chamber and beta radiation is emitted in all directions Interpretation of particle tracks from a bubble chamber The radius of curvature of the helical course of the particle depends on the charge to mass ratio, however with subatomic particles that have a charge of 1, the radius of curvature can be said to be proportional to the particles momentum. A particle with greater momentum moving through a magnetic field will be deflected less. The direction will also give an indication of the direction of the charge.

The pions directed through this bubble chamber hit other nuclei creating more particles Diagram showing paths of particles through a bubble chamber Anthony Cameron


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Appendix 1

– Uncertainty and error

Uncertainty – accuracy of readings x %uncertainty= ×100 x range of values %uncertainty= 2×average value x 1− x 2 uncertainty= x x −actual uncertainty= 1 actual Ruler = ±1mm Micrometer = ±0.01mm Vernier calliper = ±0.1mm

Appendix 2 – AS and A2 Experiment Diagrams Experiments – Units 1 and 2 Measure of gravitational pull

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Conservation of Momentum

Experiment to measure the specific heat capacity of water

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Experiment to measure the specific heat capacity of an aluminium block

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Experiment to measure the specific latent heat of fusion

Acceleration/ of a trolley

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Experiment to measure the specific latent heat of vaporisation

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Experiment to measure the effect of temperature on pressure

Experiment to measure the effect of pressure on volume

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Experiments – Units 4 and 5 Experiments involving waves Polarisation, superposition and stationary waves Effect of a polarised in the path of plane polarised light

A polaroid is placed in front of a light source, two in line if the the source is non-polarised (the first plane polarises the light. The polaroids are placed so light is detected, if two polaroids are used they must be inline. The polaroid is rotated, as it is rotated the intensity of light will diminish when the polaroid has been rotated 90O, i.e. the two polaroids are at right angles.

Experiment showing two slit superposition using microwaves and calculation of wavelength

A polarised light source, i.e. a microwave source is placed facing two slits. A probe is placed a distance away from the slits on the other side. As it is moved left and right there will be maxima and minima. The nth maxima is taken and a measurement of distance from the central maxima is taken. The wavelength will be this distance divided by n.

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Creating a standing wave using microwaves

and using this to calculate wavelength

A reflective surface is placed in front of a polarised source, such as a microwave transmitter. It will create a standing wave. By moving a probe between the transmitter and the reflective surface (slightly above it), maxima and minima can be found. The wavelength can be found by measuring the distance of the nth maxima, the wavelength equals twice the distance divided by n. λ = 2dn-1

Creating a standard wave Attach a string under tension (this is done using a pulley and a hanging mass) to a vibration generator, adjust frequency using a signal generator until a standing wave is created.

Experiments involving pendulums Measure the effect on the period of a pendulum (T), if pendulum length (l), mass (M) or starting angle (θ) is changed.

Hang the pendulum, pull it back and measure the time taken for the pendulum. Measure the time, T, taken for N oscillations. Change the mass of pendulum, starting angle or length of pendulum and repeat again measuring the time for N oscillations. Multiple oscillations are measured as this gives greater accuracy Draw graphs of results if l is variable use T2 as T ∝ √l

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Experiments involving the emission of photoelectrons Photocell experiments

Two possible setups. They use different methods to vary voltage ↑ uses a variable power supply ← uses a variable ammeter Experiment to measure stopping potential Shine a light of known frequency at the photocell cathode. Start with a high voltage and decrease until current equals zero. The magnitude of this voltage is the stopping potential, Vs, and qVs = hf – ϕ This can also be used to calculate the work function, ϕ. Experiment to find saturation point Shine an ultraviolet light at the photocell cathode. Start with a low voltage and increase. Draw a graph of current against voltage The saturation point is where the graph levels and further changes in voltage lead to no change in current. As this is when all electrons reach the anode.

A gold leaf electroscope can be used to show the photoelectric effect. A zinc plate is cleaned of its oxide layer, placed on top of the electroscope and negatively charged. Initially the leaf will be up When subjected subjected to photons from light (UV), the leaf will slowly fall down.

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Appendix 3 – Units and symbols Base SI units SI Unit

is a Measure of ...

SI Unit

kg (kilograms) ⇒ Mass

is a Measure of ...

cd (candela)

⇒ Luminosity

m (metres)

⇒ Distance

mol (moles)

⇒ Amount of a substance4

s (seconds)

⇒ time

K (kelvin)

A (Amperes)

⇒ Electric Current

⇒ Thermodynamic Temperature

Common derived units C ⇒ Coulomb F ⇒ Farad

J ⇒ Joule

N

Ω ⇒ Ohm

V ⇒ Volts

Wb ⇒ Weber

T ⇒ Tesla

⇒ Newton

Symbols and their units 56 of them (so most, not all of them), labelled alphabetically Greek letters were organised by the first letter of their name Φ – phi; λ – lambda; ω/Ω – upper and lower case omega; σ – sigma; ε – epsilon; ρ – rho A to N

N to X

a

⇒ Acceleration (m s-2)

n

A

⇒ Activity (s-1)

O ⇒ Moments (N m)

A

⇒ Cross sectional area (m2)

Ω ⇒ The density parameter (the Average massenergy density of the universe)

c

⇒ Specific heat capacity (J kg-1 K-1)

p

⇒ Momentum (kg m s-1)

C

⇒ Capacitance (F)

p

⇒ Pressure (N m-2)

P

⇒ Power (J s-1)

⇒ Mean square speed (m2 s-2)

⇒ Charge carrier density (m-3)

d

⇒ Distance (m)

ρ

⇒ Resistivity (Ωm)

D

⇒ distance

ρ

⇒ Resistivity (Ω m)

E

⇒ Energy (J)

Φ ⇒ Work function (J)

e

⇒ Charge of an electron (C)

ρ

Eε

⇒ Electromotive force (V)

Q ⇒ Charge (C)

Ek

⇒ KE of a photo electron (J)

q

F

⇒ Force (N)

R ⇒ Resistance (Ω)

f

⇒ Frequency (s )

f0 g

⇒ Density (kg m-3) ⇒ Individual charge (C)

r

⇒ Radius (m)

⇒ Threshold frequency (s )

s

⇒ Distance (m)

⇒ Gravitational field strength (m s-2)

σ

⇒ Conductivity (Ω-1 m-1)

t

⇒ Time (s)

-1

-1

GPE ⇒ Gravitational potential energy H0

⇒ Hubble constant (s-1)

T ⇒ Temperature (K)

I

⇒ Impulse (N s)

t½ ⇒ Half life (s)

I

⇒ Current (A)

u

4 Subject to Avogadro's number

NA ≈ 6.022 x 10^23

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I

⇒ Intensity (W m-2)

U ⇒ Internal energy (J)

KE

⇒ Kinetic Energy

v

l

⇒ Specific latent heat (J kg-1)

V ⇒ volume (m3)

l

⇒ Length (m)

V ⇒ Potential Difference (V)

L

⇒ luminosity

v

λ

⇒ Decay constant (s-1)

W ⇒ Work done (J)

λ

⇒ Wavelength (m)

ω ⇒ Angular velocity (s-1)

N

⇒ number of moles (mol)

x

⇒ Velocity / final velocity (m s-1)

⇒ Drift velocity (m s-1)

⇒ Displacement (m)

Units missing from previous table (mainly do to with magnetic fields) B ⇒ Magnetic flux density (T) N ⇒ Number of turns on a coil e

⇒ Electric field strength (N C-1)

n

⇒ Number of coil turns per unit length

λ

⇒ Magnetic flux linkage (Wb)

Φ ⇒ Magnetic flux (Wb)

μ0

⇒ Permeability of free space

Appendix 4 – Metric prefixes Common metric prefixes at A-level

Prefix Symbol Magnitude 10x


Giga-

G

9

centi-

c

-2

Mega-

M

6

mili-

m

-3

kilo-

k

3

micro-

μ

-6

All Other metric prefixes; common, rare and unused



Yotta-

Y

24

deci-

d

-1

Zetta-

Z

21

cent-

c

-2

Exa-

E

18

mili-

m

-3

Peta-

P

15

micro-

μ

-6

Tera-

T

12

nano-

n

-9

Giga-

G

9

pico-

p

-12

Mega-

M

6

femto-

f

-15

myria-

my

4

atto-

a

-18

kilo-

k

3

zepto-

z

-21

hecto-

h

2

yocto-

y

-24

deka-

da

1

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Appendix 5 – Formula sheet Unit 1 – Mechanics and radioactivity equations Kinematic equations 1 v=uat v 2 =u 22as s=ut  at 2 2 Mechanics p=mv m V

=

F =ma P=

F=

mv – u  t

I =Ft =m v – u

O= Fd

F A

Energy, Power and Work 1 PE=mgh KE= m v 2 2

P=Fv

W = Fx = “ Mechanical work”

P=

I=

l A

=

Q t

W t

W = Ivt = “ Electrical work”

Unit 2 – Electricity and thermal physics equations Electricity Q= It I =nAqv R=

1 s= uv t 2

P=IV

W P E = =∑ p.d.= = Q Q I

Gases pV =NR T

1 pV = Nm 〈c 2 〉 3

Thermal physics E=mc t

E=ml

V =E−IR

−1

P=

Nm V

 U =Q W

R t=R1 R2... Rn ⇒ Series 1 1 1 1 =  ... ⇒ Parallel R t R1 Rt Rn 1 p= P 〈 c2 〉 3 0

 C =273 K

Unit 3A – Astrophysics equations L= T 4 A I=

max T =2.898×10−3

L 2 4D

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Unit 4 – Waves and our universe equations Circular motion v=r x=2 r v=

2 r T

T=

1 f

a=

Simple harmonic motion x= x 0 cos t 

=

2r =r  2 2 T

F =−kx dx v= =− x 0 sint  dt

 2 = t T

a=− 2 x

dv 2 =− x 0 cos t dt

a=

SHM – Springs and pendulums =



k m



T =2



m k

T =2

Light and wave particle duality v= f  E=hf I=

P 4 r 2

=

The universe v= H 0 D

E k =E−

=hf 0

h p

x  = D s

T =H −1

Unit 5 – Field and forces equations Gravitational fields G m1 m2 F GM F= g= = 2 2 m r r

Electric fields k Q 1 Q2 F= r2 W =QV

Capacitance 1 1 1 1 =  ... Ct C1 C 2 Cn C t =C 1C 2...C n

series parallel

C=

Q V

E= 



F V kq = = Q x r2

B=

=BA

0 I 2r

=N 



k=

1 4 0

1 me v 2 =e V 2

1 E= QV 2

Magnetic fields

F =BIL



l g

=− dtd  N =−B l v

Vp Np = Vs Ns

B=0 n I

Unit 6 – Synthesis equations E=c2  m

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Alphabetical Index Accelerators........................................................................................................................................ 38 alpha radiation...................................................................................................................................... 4 Analogies............................................................................................................................................ 36 Angular Speed.................................................................................................................................... 16 Atmospheric effects............................................................................................................................12 AU...................................................................................................................................................... 13 B-field.................................................................................................................................................32 Background radiation........................................................................................................................... 4 beta radiation........................................................................................................................................ 4 big bang.............................................................................................................................................. 26 Black hole........................................................................................................................................... 14 Browninan motion.............................................................................................................................. 10 bubble chambers................................................................................................................................. 40 Capacitance.........................................................................................................................................30 capacitor............................................................................................................................................. 30 capacitor charging.............................................................................................................................. 31 Capacitor discharge............................................................................................................................ 37 capacitor discharging..........................................................................................................................31 capacitor, energy stored......................................................................................................................31 Capacitors in parallel.......................................................................................................................... 30 Capacitors in series.............................................................................................................................30 carbon-12............................................................................................................................................ 38 CCD, Charge coupled devices............................................................................................................12 Cepheid variable stars.........................................................................................................................13 Cetnripetal force................................................................................................................................. 16 Charge...................................................................................................................................................6 Charge carrier density...........................................................................................................................6 closed universe................................................................................................................................... 26 cloud chambers................................................................................................................................... 40 COBE, Cosmic Background Explorer................................................................................................12 Coherence........................................................................................................................................... 21 Cold sink.............................................................................................................................................11 Colliding beam experiments...............................................................................................................38 Comparison of capacitance with resistance........................................................................................30 Comparison of capacitor discharge and radioactive decay................................................................ 37 Comparison of electric and gravitational fields..................................................................................36 Comparison of springs and capacitors................................................................................................36 Compressions..................................................................................................................................... 19 Conductivity......................................................................................................................................... 8 conservation of energy....................................................................................................................... 34 Conservation of energy.............................................................................................................9, 11, 20 Conservation of energy, Principle of....................................................................................................3 Conservation of mass energy..............................................................................................................38 Conservation of Momentum...............................................................................................................43 constructive interference.................................................................................................................... 20 critical density.................................................................................................................................... 26 cross sectional area............................................................................................................................... 6 Current.................................................................................................................................................. 6 Anthony Cameron


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Cyclotron............................................................................................................................................ 39 DeBroglie........................................................................................................................................... 25 decay constant...................................................................................................................................... 4 Density..................................................................................................................................................3 derived units....................................................................................................................................... 51 destructive interference...................................................................................................................... 20 Detecting neutral particles.................................................................................................................. 40 detecting particles............................................................................................................................... 39 Diffraction.......................................................................................................................................... 20 diffraction gratings............................................................................................................................. 25 Doppler shift....................................................................................................................................... 26 drift chambers..................................................................................................................................... 39 Drift velocity........................................................................................................................................ 6 E.M.F. (Electromotive forces)..............................................................................................................8 Eddy currents......................................................................................................................................35 Efficiency of a heat engine................................................................................................................. 11 Electric field strength......................................................................................................................... 29 Electric fields......................................................................................................................................29 Electrical potential difference...............................................................................................................8 Electrical work....................................................................................................................................11 Electricity............................................................................................................................................. 6 Electromagnetic induction..................................................................................................................34 electromagnetic spectrum, the............................................................................................................ 18 Electromagnetic waves....................................................................................................................... 18 Electron beams................................................................................................................................... 30 energy flux..........................................................................................................................................20 Energy levels...................................................................................................................................... 24 Energy, capacitor................................................................................................................................ 31 Equipotential surfaces........................................................................................................................ 28 error.................................................................................................................................................... 42 exponential rate.................................................................................................................................... 4 Farad................................................................................................................................................... 30 Faraday cage....................................................................................................................................... 36 Faraday's law...................................................................................................................................... 34 field strength.................................................................................................................................... 28p. Fields.................................................................................................................................................. 28 final contraction..................................................................................................................................27 Fission.................................................................................................................................................38 Fixed target experiments.................................................................................................................... 38 Fleming's left hand rule...................................................................................................................... 32 flux linkage......................................................................................................................................... 34 Forces................................................................................................................................................... 2 Free body force diagrams..................................................................................................................... 2 Frequency........................................................................................................................................... 16 fusion.................................................................................................................................................. 14 Fusion................................................................................................................................................. 38 gamma radiation................................................................................................................................... 4 Giant molecular cloud........................................................................................................................ 14 Gold leaf electroscope........................................................................................................................ 50 Gravitational field strength.................................................................................................................28 Gravitational fields............................................................................................................................. 28 Gravitational Potential Energy............................................................................................................. 3 Anthony Cameron


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Half life.................................................................................................................................................4 Hall effect........................................................................................................................................... 33 Hall probe........................................................................................................................................... 33 Heat.....................................................................................................................................................10 Heat pump.......................................................................................................................................... 11 Heating............................................................................................................................................... 11 Hertzsprung-Russel Diagram............................................................................................................. 13 Hot source...........................................................................................................................................11 Hubble telescope................................................................................................................................ 12 Hubble's constant................................................................................................................................26 Hubble's law....................................................................................................................................... 26 Hydrogen atom, stationary waves...................................................................................................... 25 Ideal gases.......................................................................................................................................... 10 indefinite expansion of the universe...................................................................................................27 infinitely long straight wire, Flux density.......................................................................................... 33 Insulators.............................................................................................................................................. 7 intensity.............................................................................................................................................. 20 Intensity.............................................................................................................................................. 12 Internal energy....................................................................................................................................11 Internal resistance................................................................................................................................. 9 Interpretation of particle tracks from a bubble chamber.................................................................... 41 Interpretation of particle tracks from a cloud chamber...................................................................... 41 Inverse square law.............................................................................................................................. 20 IRAS, Infra red Astronomical Satellite.............................................................................................. 12 isotopes................................................................................................................................................. 4 Kepler's three laws of planetary motion............................................................................................ 28 Kinematics............................................................................................................................................ 2 Kinetic Energy......................................................................................................................................3 Kinetic model of matter......................................................................................................................10 Kirchoff's first law................................................................................................................................ 6 Kirchoff's second law........................................................................................................................... 9 Laws of thermodynamics................................................................................................................... 11 LDRs (Light Dependant resistors)........................................................................................................9 left hand rule.......................................................................................................................................32 Lenz's law........................................................................................................................................... 34 light year............................................................................................................................................. 26 Linear momentum................................................................................................................................ 3 Linear particle accelerators.................................................................................................................38 linear response.................................................................................................................................... 12 Longitudinal Waves............................................................................................................................19 Luminosity..........................................................................................................................................12 magnetic field line.............................................................................................................................. 32 Magnetic fields................................................................................................................................... 32 Magnetic flux......................................................................................................................................34 Magnetic flux density......................................................................................................................... 32 Magnetic Flux linkage........................................................................................................................ 34 mass-energy density........................................................................................................................... 26 Mechanical energy................................................................................................................................3 Mechanical oscillators........................................................................................................................ 17 Mechanical work................................................................................................................................ 11 Metals................................................................................................................................................... 7 Metric prefixes....................................................................................................................................52 Anthony Cameron


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moments............................................................................................................................................... 2 momentum............................................................................................................................................ 3 Monochromatic...................................................................................................................................21 Natural frequency............................................................................................................................... 17 Nebulars..............................................................................................................................................14 neutral particles.................................................................................................................................. 40 Neutral point....................................................................................................................................... 32 Neutron star........................................................................................................................................ 14 Newton's First Law of motion.............................................................................................................. 2 Newton's Third law of motion.............................................................................................................. 2 Newton's three laws of motion............................................................................................................. 3 Newton’s second law of motion........................................................................................................... 3 Nuclear Fission................................................................................................................................... 38 Nuclear Fusion....................................................................................................................................38 open universe......................................................................................................................................26 Optical line spectra............................................................................................................................. 26 Ordered and disordered processes...................................................................................................... 11 Parallax............................................................................................................................................... 13 Parallel circuits..................................................................................................................................... 9 Path difference....................................................................................................................................20 Peak wavelengths............................................................................................................................... 12 pendulums...........................................................................................................................................49 Pendulums.......................................................................................................................................... 16 Period..................................................................................................................................................16 Permanent magnets.............................................................................................................................32 Phase...................................................................................................................................................20 Photocell............................................................................................................................................. 50 photoelectron...................................................................................................................................... 22 photoelectrons.....................................................................................................................................50 photoemmisive cell.............................................................................................................................23 pi-mesons............................................................................................................................................41 pions................................................................................................................................................... 41 Plane polarisation............................................................................................................................... 19 point charges.......................................................................................................................................29 point masses........................................................................................................................................28 Polarisation................................................................................................................................... 19, 48 Potential difference graphs................................................................................................................... 8 Potential divider....................................................................................................................................9 Power.................................................................................................................................................... 3 Power dissipation..................................................................................................................................8 Pressure...............................................................................................................................................10 Progressive waves.............................................................................................................................. 19 Projectiles............................................................................................................................................. 2 proton-proton chain............................................................................................................................ 14 Protostars............................................................................................................................................ 14 pulsar.................................................................................................................................................. 14 Quantum phenomena..........................................................................................................................22 radial fields...................................................................................................................................... 28p. radioactive decay................................................................................................................................ 37 Radioactive decay.................................................................................................................................4 Radioactivity.........................................................................................................................................4 Rarefactions........................................................................................................................................ 19 Anthony Cameron


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Red giants........................................................................................................................................... 14 Resistance............................................................................................................................................. 8 resistivity.............................................................................................................................................. 8 Resonance...........................................................................................................................................17 right hand rule..................................................................................................................................33p. Ring accelerators................................................................................................................................ 39 Saturation point.................................................................................................................................. 23 Semi-conductors................................................................................................................................... 7 Series circuits........................................................................................................................................9 SHM, Simple harmonic motion..........................................................................................................16 SI units................................................................................................................................................51 sinusoidal............................................................................................................................................ 20 solenoid...............................................................................................................................................33 spark chambers................................................................................................................................... 39 Specific heat capacity......................................................................................................................... 10 specific heat capacity of an aluminium block.................................................................................... 44 specific heat capacity of water............................................................................................................43 Specific latent heat............................................................................................................................. 10 specific latent heat of fusion...............................................................................................................45 specific latent heat of vaporisation..................................................................................................... 46 Springs................................................................................................................................................ 17 Standing waves in Hydrogen..............................................................................................................25 Star classes, Summary........................................................................................................................ 15 Stars................................................................................................................................................. 12p. Stationary waves.................................................................................................................................19 Stefans constant.................................................................................................................................. 12 Stellar Nursery....................................................................................................................................14 Stopping potential...............................................................................................................................23 super giants......................................................................................................................................... 14 Supernovae, type II.............................................................................................................................14 superposition.......................................................................................................................................48 Superposition...................................................................................................................................... 20 Surface temperature............................................................................................................................12 Symbols.............................................................................................................................................. 51 Tesla................................................................................................................................................... 32 The heat engine...................................................................................................................................11 The nuclear atom.................................................................................................................................. 5 The photoelectric effect...................................................................................................................... 22 Thermistors...........................................................................................................................................9 time constant.......................................................................................................................................37 Time Period........................................................................................................................................ 16 transformer......................................................................................................................................... 35 Transverse waves................................................................................................................................19 two slit superposition using................................................................................................................ 48 u.......................................................................................................................................................... 38 Uncertainty......................................................................................................................................... 42 uniform............................................................................................................................................ 28p. Wave particle duality..........................................................................................................................25 Wave properties of electrons.............................................................................................................. 25 wavefront............................................................................................................................................ 20 Waves................................................................................................................................................. 18 Weber................................................................................................................................................. 34 Anthony Cameron


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White dwarf stars................................................................................................................................14 Wiens Law..........................................................................................................................................12 wire..................................................................................................................................................... 33 wire chamber...................................................................................................................................... 39 work function......................................................................................................................................50 Work function.....................................................................................................................................22 Young's double slit experiment.......................................................................................................... 21

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A2 and AS Level Physics Notes

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