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Physics 208: Electricity and Magnetism Exam 2, Secs. 506–510 5 Mar. 2003
Instructor: Dr. George R. Welch, 415 Engineering-Physics, 845-7737
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IMPORTANT
Read these directions carefully:
• There are 5 problems totalling 100 points. Check your exam to make sure you
have all the pages. Work each problem on the page the problem is on. You
may use the back. If you need extra pages, I have plenty up front.
• Indicate what you are doing! We cannot give full credit for merely writing
down the answer. Neatness counts! I will give generous partial credit if I
can tell that you are on the right track. This means you must be neat and
organized.
• Each problem with its associated figure is self explanatory. If you must ask
a question, then come to the front, being as discrete as possible so as not to
disturb others.
• Put your name on each page it is asked for. You will lose credit if you fail to
print your name on each page it is asked for.
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Physics 208: Electricity and Magnetism, Exam 2
Problem 1. 20 points.
Consider the circuit shown below. The capacitance of all three capacitors is C. That means that
C1 = C2 = C3 = C. The potential difference between points a and b is V . After all the capacitors
are fully charged, the switch is thrown to the right. What is the final charge and potential difference
across each capacitor?
S
a
C2
V
C1
C3
b
Hint: The final charges on C2 and C3 are equal, and the potential differences across them are
equal. So, you only need to calculate the final charge on C1 and C2 , and the potential differences
across them.
This means you are calculating 4 things. Draw a box around each answer.
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Physics 208: Electricity and Magnetism, Exam 2
Problem 2. 20 points.
A hollow cylindrical resistor with inner radius r1 and outer radius r2 , and length L, is made of
a material whose resistivity is ρ.
r2
r1
L
(a) (5 points) Suppose current flows along the length of the cylinder (left to right in the Figure.)
Calculate the resistance of this cylinder.
(b) (15 points) Suppose current flows radially outward from the inner radius to the outer.
(One might arrange such a current by lining the inside and outside with very good conductors,
and applying a potential difference between them.) Calculate the resistance for current that flows
radially outward.
Hint: Divide the resistor into concentric cylindrical shells and integrate.
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Physics 208: Electricity and Magnetism, Exam 2
Problem 3. 20 points.
Consider the DC circuit shown below. Calculate the current in each resistor.
V
R
2R
V
3R
Note: Draw a box around each of the three answers. Make sure it is clear to me which answer
goes with which resistor.
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Physics 208: Electricity and Magnetism, Exam 2
Problem 4. 20 points.
Consider the circuit shown below. Assume the following numerical values for the components:
V = 30 V, R1 = 6 Ω, R2 = 3 Ω, and C = 1 µF.
R1
V
S
R2
C
(a) Suppose that the switch S is open and we wait a long time, so that the capacitor is fully
charged. Calculate the charge on the capacitor.
(b) Now, suppose that the switch S is closed. (Assume the battery is removed.) How long will
it be before the charge on the capacitor has dropped to 10 percent of the value calculated in part
(a)?
Note: You may write your answer in terms of the natural log of 10, ln 10. The arithmetic is very
simple – if you really need a calculator, then you are probably doing it wrong.
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Physics 208: Electricity and Magnetism, Exam 2
Problem 5. 20 points.
Consider the circuit shown in the Figure. A 50 Volt battery is connected through a 2 Ω resistor.
The wire connecting them passes through a region of homogeneous magnetic field of magnitude
B = 4 Tesla. The wire passes a distance a = 6 cm into the field, and then bends 90◦ and goes a
distance b = 8 cm before leaving the field.
Calcuate the magnitude of the net force on the wire.
Warning! Warning! Warning! Force is a vector. I want the magnitude of this vector.
V=50
b
R=2
a
Magnetic Field B=4T
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