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EXAM 1
February 19, 2004
Name:____________________
Rules for Exam:
1. Calculators are allowed, but you may not share one.
2. Show your work on non-multiple choice problems. NO WORK=NO CREDIT.
3. Include units with each answer. One point deduction per infraction.
4. Points will be deducted for students that refuse to turn in their exams, when asked to do so (at
the end of class).
5. Round off to 2 decimal places and circle your final answers.
6. Circle your final answers.
Good Luck!
Equations, Conversion Factors and Constants:
k=8.99x
9
Nm
2
/C
2
o=8.85x
C
2
/Nm
2
1 C=
6
C=
3
nC=
6
pC
mp=1.67x
kg; me=9.11x
kg
e=1.60x
C
1eV=1.60x
J
Scores
Part 1 (17 pts)
Prob 1 (12 pts)
Prob 2 (12 pts)
Prob 3 (17 pts)
Prob 4 (12 pts)
Prob 5 (12 pts)
Prob 6 (23 pts)
TOTAL (105 max)
% (out of 100)
2 2
2 2
2 2
2 2 2
2 2
2
2 2
2 2
2 2
2 2
x x a
x a
dx
x x a
x x a a
x a
x dx
x a
x a
xdx
x a
x a
xdx
ln
ln
ln
Multiple choice and short answer questions (3 points each, unless noted)
1. In each of the cases shown below, the charge and separation of the objects is the same. In
which case is the force between the two charged objects the least?
A.
B.
C.
2. A dipole is oriented perpendicular to a uniform electric field as shown. The magnitudes of the
net force and torque on the dipole, respectively, are
A. 2qE, 0
B. 0,qLE
C. qE, qLE
D. 2qE, 2qLE
E. 0, 2qLE
3. If the electric potential V(x,y)=3xy, then the electric field vector is expressed as
A.
3 y
i 3 x
j
B.
i 3
j
C.
3 x
ˆ i
D.
i 3
j
E. 0
4. A charge +q is located at the center of a cube having sides of length L. A second charge +q is
placed at the center of a cube having sides of length 0.5L. As a result, the flux through the
smaller cube is
A. one-eighth that of the large cube.
B. one-fourth that of the large cube.
C. the same as that of the large cube.
D. four times that of the large cube.
E. eight times that of the large cube.
C,B,A,C
+q +q
Insulatin
g Sphere
Charge
+q
+q
+q
Conducting
Sphere
Charge
+q
-q
+q
E
L
- A group of four charges is arranged to form a square of side L. Calculate the magnitude of
the electric field on a charge placed at the midpoint of one of the sides of the square, if
q=1.25nC and L=0.30m (12 points).
911N/C
- Calculate the potential energy of the charge in the lower left corner of the configuration of
charges shown above if q=1.25nC and L=0.30m. How much work is required to move this
charge from its current position to infinity without any change in kinetic energy (12 points).
6.06x
-
J
-q
L
+q
-q +q
- A rod is bent into a semicircle of radius R=0.20m and uniformly charged with a total charge
Q=6.28nC (see below). If the center of the semi-circle is located at the origin, calculate the
electric field at the origin (12 points).
-900iN/C
- Calculate the electric potential at the point P on the axis of the annulus shown below, which
has uniform surface charge density (12 points).
2 kQ
b
2
a
2
x
2
b
2
x
2
a
2
P
a
b
x
x
y
R
+
-
+
-
