CP3 Exam 1 Study Guide 20103
Exam 1
Friday, 25 March
Page 1 of 7
110 minutes
Bring to the exam: y harged calculator C harged y uler R uler NOTE: IN ADDITION TO THIS STUDY GUIDE, YOU AR E EN C OU R TO LOOK OVE R C OU R AGED R THE SOLUTIONS TO EXAM 1 GIVEN DU R TE R OU R SES. RING ING WINTE R R QUAR TE R 20102. THESE AR E POSTED ON MY C C OU R SES.
NOTE: THIS P R OBLEM WAS DONE IN DETAIL IN C LASS. LASS. R OBLEM SEE YOU R R OWN NOTES FOR SOLUTION.
Two charged spheres are hanging by threads threads from a singles point above them. The length of each thread is 10.0 cm and the separation between the spheres is also 10.0 cm. The mass of each sphere is 2.00 grams. (a) Draw the system (similar to an equilateral triangle) which is identical to the one we studied in class. (b) Draw a free body diagram for the right hand sphere. (c) Write down Newton¶s 2nd Law equations for static equilibrium. (d) Solve the equations for F t, the magnitude of tension force in the thread, and the |q|, the magnitude of one of the identical charges. (0.0226 N, 1.12 v 10-7 C) Field line sketching: USE METHOD OF 8 ³OPENINGS´ PE R HAR GE GE Q F R OM C LASS LASS R C HA R OM (a) Sketch the field lines for a dipole distribution +q and -q which are separated by a distance d. Use 8 field lines for charge q. (b) Sketch the field lines for the t he distribution +q and + +qsep qseparated arated by a distance d. (c) Sketch the field lines for the distribution distribution ±q and +2q separated by a distance distance d. (d) How is it possible to create an electric field which is approximately uniform over a certain region of space? Explain with a picture. picture. Units: The SI units are meters, kilograms, seconds, and coulombsm, coulombsm, kg, s, C Know the basic definitions definitions of the SI units for the Newton, the Joule, the Volt. Know the two SI units which can be used for the electric field and how to show that they are equivalent.
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CP3 Exam 1 Study Guide 20103
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NOTE: A SIMILAR P R OBLEM TO THIS P R OBLEM WAS DONE IN DETAIL IN C LASS. In order to print this document from Scribd, you'll first need to download it.
5 nm
y-axis
(nm)
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x-axis
(nm)
5 nm Given an electron at the point x = +4.00 nm on the x-axis. Let the test point P be at y = +3.00 nm on the y-
axis. Note: 1 nanometer = 1 nm = 10 -9 meters.See formula sheet for the mass and charge of the electron. (a) Sketch the electric field vector at the point P.Label the magnitude |E|, the Xcomponent E x and the Ycomponent E y . (b) C alculate the x and y components of the electric field at the point P. |E| = 5.76 v10 7 N/ C , E x = + 4.61 v 10 7 N/ C , E y = ± 3.46 v 10 7 N/ C
Suppose a proton is placed at the test pointP. (c) Sketch and label the force on this proton on the above diagram. Label the magnitude |F|, the Xcomponent F x and the Ycomponent F y . (d) Use the electric field definition to calculate the magnitude |F|, the Xcomponent F x and the Ycomponent F y . Use F x = qE x , F y = qE y, and |F| = |q| |E|
y
Use Newton¶s Second Law to determine the SI units for force in terms of the m, kg, and s.
y
Use the equation that defines the electric field to determine the SI units for the electric field.
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to Example 20.5 Finding the f ield on the axis of a
Given q ±=
In order to print this document from Scribd, you'll
x = ±1.50 nC ±0.600 cm firstat need to download it. a nd q + = + 1.50
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nC
dipole
at x = 0.600 cm.
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(a) Show that at the point x = + 1.80 cm, the net electric field is E dipole= [ 7.02 v 104 N/C, toward + X ] This is the same problem done in class. Here, the origin of the x axis is midway between the two charges which are separated by 1.20 cm. The observation point P is 1.20 cm to the right of the positive charge. (b) If an electron were placed at the observation point P, what would the electric force on it be? Give direction and magnitude. y
Similar to Example 20.5 Finding the field off the axis of a dipole y
Given q ±= ±1.50 nC at y = ± 0.600 cm and q+ = + 1.50 nC at y = 0.600 cm. (a) Show that the net electric field at the observation point (x = +2.40 cm, y = 0.00 cm) is E dipole = [1.07 v 10 4 N/ C , toward negative Y ] (b) If an electron were placed at the observation point P, what would the electric force on it be? Give direction and magnitude. (c) Use the parallelogram rule to find the net dipole field at the point shown and at other off axis points in the XY plane.R efer to in-class worksheet.
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P R OBLEM From WOR KSHOP: Parabolic motion of an electron in an e lectric field. In order to print this document from Scribd, you'll
4 v 10 N/ C between two very long parallel horizontal conducting Given a uniform electric field 2.00 y = ±to firstE need download it. plates. The top plate is 3.00 meters above the x-axis and the bottom plate is 3.00 meters below the x-axis. At timet = 0, the electron is at the origin and moving in the positive x-direction with a speed of 5.00 v 10 7 Cancel Download And Print m/s. (a) Make an accurate and labeled sketch of the information provided.
(b) Draw the electric field lines on your sketch. (c) Sketch and label the force on the electron when it is at the origin. (d) Sketch the trajectory of the electron. Show the force on the electron at three points of the trajectory. (e) How long will it take the electron to hit one of the plates? (4.13v 10 -8 s)
(f) What are the x and y components of the velocity of the electron when its hits one of the plates? (5.00 v 10 7 m/s, 1.45 v 10 8 m/s)
(g) What are the X and Y coordinates of the electron when it hits one of the plates?(2.07 m, 3.00 m)
(h) Explain with a simple calculation why we can neglect the force of gravity in this problem. ( C ompare the acceleration ay = 3.44 v 10 15 m/s2 to g = 9.80 m/s2 . Which is bigger and by how much?)
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NOTE: A SIMILAR Problem to THIS P R OBLEM WAS DONE IN DETAIL IN C LASS. In order to print this document from Scribd, you'll y-axis first need to download it.
5.00 m
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2q
A
B
x-axis
C
Given the two charges q 1= ± 2 q and q2 = +q where ³q´ is a positive number. (a) Sketch and labelE 1 (the field due to q1 ) , E 2 (the field due to q2 ) , and E = E 1 + E 2 at the points A , B , and C on the x-axis of the above drawing. At each point, be sure that the magnitudes of E 1 and E 2 have the correct relative size. (b) Based on part (a), the total field can be zero only in one of the following region of the x-axis. (circle one):
(1) x< 0
(2) 0
(3) x> 5 m
(c) Setup and solve, the quadratic equation to determine the x-coordinate of the point P on the x-axis where the total electric field is zero. The solution is in R egion (3)atX = + 17.1 m. (There is another root in R egion (2) at X = 2.93 m, which represents a point where E 1 and E 2 are equal in magnitude but point in the same direction.)
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Suppose there is a proton (mass = 1.67 v 10 -27 kg, q = + e) in the potential field of an Iron nucleus (mass 9.40 v 10 -26 kg, q = + 26 e). §
(a)
C alculate the potential of an iron nucleus at a radial distance of 15.0 nm.
(This is the potential on
the inner circle above.) 2.49 Volts (b)
C alculate
the potential of an iron nucleus at 30.0 nm. (This is the potential on the ³in-between´ circle above.) 1.25 Volts
(c)
C alculate the potential of an iron nucleus at 45.0 nm
(This is the potential on the outer circle
above.) 0.831 Volts (d) On the above diagram, sketch the corresponding electric field lines for the iron nucleus. (e)
C alculate the magnitude of the electric field on the ³in-between´ circle.
4.16 v 10 7 N/ C
(f) Suppose we now put a proton, initially at rest, on the inner circle above. What is the speed of the proton when it reaches the outer circle? R ecall that U =qV where U is potential energy and V is potential. Use energy conservation the way we did in class! (1.78 v 10 4 m/s)
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Six arrangements of two electric charges of equal magnitude Q, and a test charge +q at point P, are shown below. All to charges on a straight line.you'll The distances between adjacent In order print thislie document from Scribd, charges are all the same are first(the needdrawings to download it. not exactly scaled).Rank the magnitude of the net electric forces on the +q test charge at points P, from largest to smallest. Your answer should be in the form A = B > C > D = E > F (not necessarily in this order, of course).. Cancel
A Q
B Q
P (+q)
+Q
D +Q
T he
Q
C P (+q)
Q
E
+Q
P (+q)
Bohr Hydrogen
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Q
Q
P (+q)
+Q
F P (+q)
+Q
P (+q)
+Q
Atom
Part 1 Ground state orbit and energy
Given: The hydrogen atom (in its ground state) is an electron orbiting a proton at a distance of 0.0529 nm. Fundamental constants you will need: e, c , melectron, mproton, G, k = 1/(4 TI 0) *Show c omplete
calculati on setups i n d etail w it h c orr ect
sig nificant figur es.
(a)
Calculate the magnitude of the force on the electron by the proton. (8.22 × 10-8 N)
(b)
Calculate the speed of the electron. (2.18 × 106 m/s c / 137.) §
(c)
Calculate the kinetic energy of the electron in SI and ³eV´ units. (2.17 × 10-18 J, 13.6 eV)
(d)
For the electron and the proton, compare the electric force of attraction to gravitational force of attraction. (F grav / F elec = 4.4 × 10 ± 40)
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