AJM:1/6/05 Score /100
Physics 133 Midterm Fall 2003
Name
!
PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the front. Read
each problem carefully. The credit you receive on each problem will depend at least as much on how you get your answer as
on what answer you get. There is no need to be as “wordy” as I ask you to be on homework, but you must show your work
or give at least a brief explanation for every answer. I give no credit for unsupported answers. I give partial credit for
partially correct solutions, but only when I can figure out what you are doing, so am as clear as possible. Make certain that
all numerical answers are given with a reasonable number of significant digits (when in doubt, three is almost always a good
compromise!) and that you have included appropriate and simplified units. Check your answers for physical reasonableness
whenever possible; I do deduct points for obviously ridiculous answers that go uncommented upon.
1. [30 pts total] Two small objects with charges as shown are located as shown.
a) [7] Find the electric potential at position A.
b) [8] Find the amount of work that would be required to move a small object
carrying a charge of -2.0 µC from position A to position B.
c) [15] Find the direction of the electric field at position A. (Express your answer by
referring to the indicated coordinate directions.)
EXTRA CREDIT [5 pts] With only the original two objects in the vicinity, what
charge, when placed at position A, would cause the total potential energy of the three
charge system to be zero?
2. [25 pts total] In the capacitor network shown at right,
V
a−V
d=30 V
.
a) [10] Find the equivalent capacitance between points a and d.
b) [5] Find the charge on the 6.0-µF capacitor.
c) [5] Find the potential difference
V
c−Vb
.
d) [5] Find the energy stored by the 9.0-µF capacitor.
EXTRA CREDIT [5 pts] What is the equivalent capacitance between points a and c?
3. [15 pts total]
a) [10] Find the electric field (a vector!) at the position P due to the thin,
uniformly charged rod. [Hints: I suggest that you use the distance
from position P as your variable of integration. Your answer should,
of course, be expressed in terms of "the givens."]
b) [5] Suppose that all of the charge on the rod is gathered and placed at the midpoint of the rod. How would the
electric field at position P change? That is, does it get larger, smaller, or remain the same? [Hint: The easiest
thing to do here is simply to calculate the new electric field and compare it with your answer to part a.]
4. [15 pts total] As shown at right, a small object carrying a charge of +3.0
µC is located at the center of an uncharged conducting spherical shell with
inner and outer radii 5.0 cm and 10 cm. There is nothing at positions A
and P, both of which lie 15 cm from the center of the spherical shell.
a) [8] Find the amount of charge on the inner and outer surfaces of the
spherical shell.
b) [7] Find the magnitude of the electric field at position P.
EXTRA CREDIT [5 pts] Suppose a charge of -12 µC is now placed at
position A. Tell me what happens to the electric field at position P. (Be
as precise as you can in explaining what happens.)
5. [15 pts] Three small identical objects each with mass m = 1.0 g and charge q = 1.0 µC
are placed in a line as shown at right. The objects are then released simultaneously from
rest. How fast does the leftmost object eventually move?
3.0
µF
a
b
6.0
µF
c
d
9.0
µF
1.0
µF
P
L
L
q
(uniformly distributed)
P
A
uncharged
conducting
spherical shell
3.0
µC
5 cm
10 cm
15 cm
15 cm
10 cm
10 cm
9.0 cm
12 cm
A
B
x
y
12 cm
18.0 cm
q = 10
µC
1
q = -5.0
µC
2