AJM:5/1/05 Score /100
Physics 133 Midterm Exam Spring 2005
Name
!
Time allowed: 55 minutes. You may use one sheet of notes (8-1/2 x 11, both sides) and a calculator. No hats and no
devices with communication or photographic capabilities may be used during the exam. Work the problems on
separate sheets of blank paper and staple this sheet to the front.
Read each problem carefully and be sure to pay attention to any hints that are provided. There is no need to be as āwordyā as
I ask you to be on homework, but you must show enough work or give enough of an explanation to show me that you
understand what you are doing. I give no credit for unsupported answers. Partially correct solutions, will get partial credit,
if I can figure out what you are doing, so use plenty of space and try your best to be reasonably neat and clear. All numerical
answers must be given with an appropriate number of significant digits and appropriate, simplified units. Check your
answers for physical reasonableness; I deduct a small number of points for ridiculous answers that go uncommented upon.
1. Three small objects with charges as shown are located as shown.
a) [10] Find the magnitude of the electric force on the negative charge
b) [10] Find the direction of the electric field at the unoccupied corner of the
rectangle and express it in the conventional form, i.e. as an angle
counterclockwise from the positive x-axis.
2Three small charged objects are located at corners of a square as shown.
a) [10] Find the electrostatic potential at position A.
b) [10] Find the amount of work that would be required to move a small object with a
charge of
3.0
Āµ
C
from position A to position B.
3. a) [10] Later on we will learn that the speed of light in a vacuum is given by
c=1
Īµ
o
Āµ
o
where
Īµ
o
is the āpermittivity of free space,ā (a quantity that appears in many of the
electric formulae we have encountered) and
Āµ
o
is the āpermeability of free space,ā a quantity that will appear in our
study of magnetism. What are the physical dimensions (in terms of M, L, T, and Q) of
Āµ
o
?
b) [10] What is the name of the physical quantity that could be measured in units of
ft ā
lb
Vā
hr
? (Note: ālbā is the symbol
we use for the āpound,ā an English unit of force.)
4. In the capacitor network shown at right point a is held at a potential 30 V higher than that
of point d.
a) [10] Find the equivalent capacitance between points a and d.
b) [5] Find the charge on the 6.0 ĀµF capacitor.
c) [5] Find the potential difference
VbāVc
.
EXTRA CREDIT [5] Suppose that I remove the insulating material that previously filled
the region between the plates of the
7.0
Āµ
F
capacitor and find that the potential difference
across the
10
Āµ
F
capacitor becomes 15 V. What was the dielectric constant of the removed
material?
5. A solid nonconducting sphere of radius 2a has a total charge Q distributed uniformly
throughout its volume. A much smaller charged object is located as shown a distance 4a
from the center of the sphere. Positions A and B are located as shown, each a distance a
away from the sphereās center, C. The electric field at position A is zero.
a) [10] What is the charge on the small object?
b) [10] What is the electric field, a vector, at position B?
a
6.0
ĀµF
b
c
d
10
ĀµF
12
ĀµF
7.0
ĀµF
8.0
ĀµF
a
x
y
ā3
q
q
2
q
2
a
A
B
30
ĀµC
12 cm
ā6.0
ĀµC
ā10
ĀµC
12 cm
5.0 cm
3.0 cm
A
B
C
