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It had been found that if a rubbed amber rod was dangling from a string, and another rubbed amber rod was brought near, the dangling one would move away. ● If a dangling rubbed glass rod is brought near another rubbed glass rod, the dangling one would move away. ● If a rubbed glass rod r od and amber rod were brought near to each other, they were attracted. ● Therefore, the charge on the glass must be different from the charge on the amber! Franklin decided to say that… ● the glass rod had a positive charge ● the amber rod (or the plastic ebonite used u sed today) had a negative charge ●
Why did he choose to call glass positive and amber negative? ●
No reason! He knew they were different different and opposite to each other so he just picked one to be positive and the other o ther negative. • •
• •
All matter consists of atoms Atoms are made of a nucleus (neutron and proton) and electron/(s) revolving around the nucleus. ( ) are positively charged and are neutrally charged. are negatively charged. All charges follow the qualitative “ ”:
“ Like charges repel, unlike charges attract”
Fig.1.1
ELECTRON, − PROTON, p NEUTRON, n •
9.11 9.11 × 10−31 1.67 1.67 × 10−27 1.67 1.67 × 10−27
−1.6× 10−19 +1.6× 10−19
None
Electric Charges have two properties : •
•
•
•
All observable charges in nature occur in discrete g packets or in integral amounts of the . Any charge Q occurring in nature can be written = + When you effect a transfer of charge: If an electron goes from object A to object B, object A becomes positive and object B becomes negative. The net charge of the two objects remains constant; that is, charge is conserved. c onserved. Even in certain interactions, where charged particles are created and annihilated, the amount of charges that are produced and destroyed is equal, so there is conservation.
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• • •
Coulomb Abbr. C Type: Derived
•
Derived from the concept of current which is one of the 7 SI fundamental units
•
−1.6 × 10−19
Rubbing two different materials together, a process known as charging by friction is the simplest way to give something a charge. c harge. Since the two objects are made of different materials, their atoms will hold onto their electrons with different strengths. As they pass over each other the electrons with weaker bonds are “ripped” off one material and collect on the other material. Rub a piece of ebonite (very hard, black rubber) across a piece of animal fur. The fur does not hold on to its electrons as strongly as the ebonite. At least some of the electrons will be ripped off of the fur and stay on the ebonite. Now the fur has a slightly positive charge (it lost some electrons) and the ebonite is slightly negative (it gained some electrons).The net charge is still zero between the two… remember the conservation of charge. No charges have been created or destroyed, just moved around. Rub a glass rod with a piece of silk. This is the same sort of situation as the one above. In this case the silk holds onto the electrons more strongly than the glass. Electrons are ripped off of the glass and go on to the silk. The glass is now positive and the silk is negative •
•
•
Conduction just means that the two objects will come into actual physical contact with each other (this is why it is sometimes called “charging by contact”). c ontact”).
3. It is possible to charge a conductor without coming into direct contact with it
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4. The magnitude of the force of attraction or repulsion between two electric charges at rest was studied by Charles Coulomb. Cou lomb. He formulated a law ,known as "COULOMB'S LAW". According to Coulomb's law: •
•
The electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of charges. The electrostatic force of attraction or repulsion between two point charges is inversely proportional to the square of distance between them.
Fig.1.4 In Fig.1 there are two charges law we have
1 and 2 at a distance in air or vacuum, then by Coulomb’s 1 1 2 = 4 2 0
where , 0 is known as the “permittivity of free space”, 1 = 9.0 × 109 2 −2 4
0 = 8.86 × 10−12 2−1 −2
and
0
If the space between the charges is filled with a non conducting medium or an insulator called "dielectric", it is found that the dielectric reduces the electrostatic force as compared to free space by a factor K called DIELECTRIC CONSTANT. This factor is also known as RELATIVE PERMITTIVITY. It has different values for different dielectric materials. In the presence of a dielectric between two charges the Coulomb's law is expressed as:
= 41 1 2 2 0
or
= 41 1 2 2 where is called absolute permittivity and = 0 The magnitude as well as the direction of electrostatic force can be expressed by using Coulomb's law by vector equation:
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⃗12 = 41 1 2 2 121̂ 2 0
Where ⃗12 is the force exerted by 1 on 2 and two charges from 1 to 2 .
121̂ 2 is the unit vector along the line joining the
A charge produces an electric field in the space around it and this electric field exerts a force on any charge placed on it. The intensity of field is defined as
= ⃗ • • • •
•
is a vector field.
Travels at the speed of light. Acts on tests not on its own source Does not actually require test charges to compute
When the force and test charge (0 ) [not the source charge] values are given:
⃗ =
0
•
•
When only the the source charge ( ) [not the test charge] value is given:
= 41 2 0
The unit of E is
Let's keep in mind that you've already studied fields when you le arned about gravity. We can look at the parallels between the following two formulas to remember things about each of th em.
⃗ ⃗ =
= measurement of the strength.
⃗ =
0
field
= measurement of the strength. acting on the test ⃗ = the force acting
⃗ = the force acting on the small object. = mass of the small object (like a person), the large object (like the earth).
field charge.
= the charge of the test charge, source charge making
the
This formula measures the amount of force This formula measures the amount of force per unit charge. per unit mass.
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Just as we were able to find a connection between electrostatics and gravity as above, we can do the same thing with our new formula.
= 2
= measurement of the field strength = gravitation gr avitational al constant = mass of body producing gravitational field = distance from centre of body
• •
•
= 2
= measurement of the
We can visually represent electric fields as Caution : Electric Field lines are just imaginary – a mere representation of the electric vector field! We note that the electric field lines indicate the direction to which the force will be exerted by a positive test charge!
•
When a test charge ventures in an electric field, it experiences a force It will accelerate following Newton’s Second Law with acceleration
•
Two Kinds of Charge Distributions:
•
field strength
constant = Coulomb's constant producing electric field = charge of source charge producing = distance from centre of body
0 !
∑⃗ = =
1. Electric Dipole 2. Systems of Point Charges 2.
1. 2. 3. •
Linear: Line and Ring Charges Surface: Disk and Plane Charges Volume: Spheres and Cylinders
A combination of two charges + and − separated by a small distance of d constitutes an electric dipole.
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Fig.1.6 •
•
•
describes the strength and orientation of electric dipoles. ⃗ = ⃗
, points from the negative charge to the positive charge
Just as Forces are vectors, Fields are also vectors hence they also follow the
,
i.e. •
•
The net field at a certain point is just the vector sum of the individual contribution of each point charges = 1 + 2 + 3 + ⋯ Just like mass corresponds to its effect in density, charge can be found to exist in three spatial forms, with corresponding densities: Charge Linear charge density Surface charge density Volume charge density
•
/ / 2 / 3
We have three types of linear charges
= � (+ ) : R→ Radius of ring 2
= � 24 + : → 2
→distance from the center of the ring
2
= 2 : ℎ ℎ → y→ distance from the center L→ Length of line charge
2 3
Fig.1.7 Disks and Plane
We only consider circular disks and its infinite extension: the infinite plane = 20 1 − √ 2+2 = 20 = 2, = 1/40 R is the radius of the disk is the distance from the center of the disk
Fig.1.8
Field is measured normal to the plane
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To better understand it is a good idea to first review and figure out similarities between them. Understanding the parallels between (seemingly) unrelated things in physics is actually one of the best ways to learn physics. According to Newton’s Second Law, if a force acts on an object it will accelerate. If you drop an object, the force due to gravity will cause it to accelerate down. At the top, we can say that the object has a high ... in fact, it has its greatest potential energy at this point. While it is falling we know that the is being converted to , so that at the bottom (its reference point) it has no remaining. •
• •
•
Now if you want to move the object from its position of low potential energy to high potential energy, you must do work on the object.
Fig.1.9 The work is necessary since you are adding to the object. You would the work done using… and = = = ∵ = and =ℎ ∴ = ℎ So the work you do to change the is… = ℎ What is important to realize is that we are specifically looking at this in terms of how much work needs to be done to increase the object's potential energy, from an area where it has low potential to an area where it has high potential. potential. This change in depends on… 1. Mass of the object ( ∝ ) 2. Gravitational field strength ( ∝ g) 3. Height to which the object is moved ( ∝ ℎ) • •
•
•
•
If we follow the same ideas that we did above, you might see that there are similarities between the described above and . Lets say you place a charge in an electric field and release it.
Fig.1.10
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We expect the charge will begin to accelerate from an area of high potential energy, to an area of low potential energy. This is because there is an electric force acting on the charge. Notice that this is just like the object dropped in the discussion above; the difference is that here the reason is electrical in nature. If you want to move the charge from a position of low to high potential energy, you must do work on the object against the electric force. Again, this sounds exactly like what we were talking about above when we lifted the ball back up against the gravitational force. You would calculate it using… = and = •
• •
•
•
= This looks very much like the formula we used to figure out The change in the depends on... 1. Charge of the object ( ∝ ) 2. Electric field strength ( ∝ ) 3. Distance the object is moved parallel to the field lines ( ∝ ) •
.
•
is the change in When we were talking about , it would sort of be like saying “How much work do we have to do to lift up something against gravity per kilogram.” Something that has more mass would need more work to be done to it. Now we are measuring the ... how much work is needed per Coulomb of charge. If something has more charge, it needs more work to move it. The unit for voltage could be given in / , but instead it is a derived unit called the in honor of Alessandro Volta. This means that we have a formula for voltage that looks like this... = ∆ •
•
•
Where, = voltage (V) ∆ = electric potential energy (J) = charge (C)
Sometimes it is not convenient to measure energy in Joules. This is quite often the case when we are dealing with charges charges like electrons moving through potential differences. Instead, we can use a different unit, that although it is not part of the metric system, is still useful... the electron volt. If we look at the formula for voltage and solve it for energy, we get... ∆ = Typically we would just put in the value for the charge in Coulombs and the Voltage in Volts. Instead, we will define one electron volt as the energy needed to move one electron through one volt of potential difference. ∆ = 1 = 1(1) 1 = 1.60 × 10−19 − 19 (1) 1 = 1.60 × 10−19 If you need to do a calculation of energy in electron volts, you just figure out how many elementary charges you have multiplied by the voltage they moved through. •
•
•
When you do this, remember two things. First, “2e” does not mean 2 electrons, it mean 2 elementary charges. Second, the answer in electron volts is not a metric unit and cannot be used in any other formulas.
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We know that, an alpha particle has a 2e+ charge. ∆ = = 2(20) = 40 •
The potential at a distance r from a point charge q is given by = 41 0
dipole.
A combination of two charges + and
− separated by a small distance of d constitutes an electric
•
It is defined as a vector⃗ = ⃗ where distance vector is the vector joining the negative charge to the positive charge. The line along the direction of the dipole moment is called the axis of the dipole. Point is at distance r from the centre of the diploe ( /2) and theline joining the point P to the centre of the dipole make an angle θ with the direction of dipole movement (from – to +) Potential at P
1
= 4
2 0
where p is magnitude of electric dipole moment = . Any charge distribution that produces electric potential given by above formula is called an electric dipole. The two charge system can be expressed as = .
=
1 40
2 cos
3 1 sin = 4 3 0
Resultant electric electric field at P
= √ ( 2 + 2 ) 1 = 4 (/³)√ (3 (3 ² + 1) 0
The angle the resultant field makes with radial direction OP (O is the centre point of the dipole axis and P is that at which electric field is being calculated) is α.
= = 12 or = sin−1 12
a.
θ = 0. In this case P is on the axis of the dipole. This position is called an end-on position. = 41 as = 0 = 41 = 41 (/³)√ (3 (3 ² + 1) as = 0 2
0
0
0
2
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= 41 2 θ = 90°. In I n this case P is on the perpendicular bisector of the dipole axis. 3
0
b.
1
General formula for = 4 2 0
as θ = 90°.
= 0
1
General formula for = 4 (/³)√ (3 (3 ² + 1) as θ = 90°, 0
Angle is given by Therefore
= 90°/2 = = 90°.
1 = 4 3 0 ∞
If the dipole axis makes an angle θ with the electric field magnitude of the torque = | | = In vector notation ⃗ = ⃗ × dipole axis makes an angle with the electric field magnitude of the torque
⃗ . − If we choose the potential energy of the dipole to be zero when = 90° , above equation becomes ⃗ . () = − = −
Change in potential energy
∆ = () – (90°) = −
=
There can be no electric field inside a conductor in electrostatics. When electric field is applied from left to right some free electrons move toward the left creating a negative charge on the left surface. Due to which there will be positive charge on the right surface. Due to this charge buildup, coulomb attraction sets between these two charges and an electric field opposite in direction to the applied electric field is set up. The movement of free electrons continues till the applied electric field and the electric field due to redistribution of electrons are equal. Hence inside the conductor these two electric fields balance each other and there is no electric field inside a conductor in electrostatics. Conductors have free electrons electrons that move throughout the body. When such a material is placed in an electric field, the free electrons move in a direction opposite to the field. The free electrons are called conduction electrons in this context. In insulators, electrons are tightly bound to their respective atoms or molecules. So in an electric field, they can't leave their parent atoms. They are insulators or dielectrics. In semiconductors, at 0 K there are no free electrons but as temperature raises, small number of free electrons appear (they are able to free themselves from atoms and molecules) and they respond to the applied electric field.
