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Instructor(s): J.R. Buchler, A. Korytov
PHYSICS DEPARTMENT
PHY 2054
1st Exam
Name (print, last first):
Fall, 2005
Signature:
On my honor, I have neither given nor received unauthorized aid on this examination.
YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.
(1) Code your test number on your answer sheet (use 76–80 for the 5-digit number). Code your name on your
answer sheet. DARKEN CIRCLES COMPLETELY. Code your UFID number on your answer sheet.
(2) Print your name on this sheet and sign it also.
(3) Do all scratch work anywhere on this exam that you like. Circle your answers on the test form. At the end of
the test, this exam printout is to be turned in. No credit will be given without both answer sheet and printout with
scratch work most questions demand.
(4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not
make any stray marks or some answers may be counted as incorrect.
(5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing.
(6) Hand in the answer sheet separately.
Constants
g = 9.80 m/s2
e = 1.6 × 10−19 C
1µC = 10−6 C
−11
2
2
−31
G = 6.67 × 10
Nm /kg
me = 9.11 × 10
kg
1nC = 10−9 C
kE = 8.99 × 109 Nm2 /C2 mp = mn = 1.67 × 10−27 kg 1pC = 10−12 C
²0 = 8.85 × 10−12 C2 /N/m2
c = 3 × 108 m/s
1. An unknown charge Qc sits at the center of a thin conducting shell of inner radius equal to 2 m. The shell carries a net
charge of +3µC. Points P1 and P2 are located 1.0 m and 1.5 m, respectively from the center. If the electrical potential
difference between points P1 and P2 is ∆V = V2 − V1 = 18 kV, you deduce that the charge Qc is equal to
(1) −6µC
(2) 0
(3) +6µC
(4) −3µC
(5) +9µC
2. An electron is fired at a speed of v0 = 3 × 107 m/s and at an angle
of 60◦ with the horizontal midway between two very large parallel
planar conducting plates. The plates are a distance D = 20 cm
apart as shown in the figure. The upper plate is positively charged
and the lower plate is negatively charged in such a way that a
potential difference ∆V of 4,000 V exists between the plates. Find
the closest distance d that the electron gets to the bottom plate.
Ignore gravity.
(1) 0.4 cm
(2) 3.2 cm
(3) 0.9 cm
(4) 8.9 cm
3. A small plastic ball of mass m = 2 g, that carries a positive charge
q0 , is suspended as a pendulum with a 20 cm long insulated string
next to a large plane conductor. The conductor carries positive
surface charge of density σ on the side facing the pendulum. In
equilibrium the pendulum makes an angle of 12◦ with the vertical.
This object is now taken on a planet where the gravitational attraction is only 1/10 that on the surface of the Earth. In addition,
the charge q0 is doubled and the mass m is changed to an unknown
value. The surface charge σ is kept the same. If the equilibrium
angle of the pendulum on the planet is the same as it was on Earth,
what is the new mass [in g]?
(1) 40
(2) 20
(3) 1
(5) 5.7 cm
g
12o
q0, m
+σ
(4) 0.05
(5) 0.025
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4. A positive charge of +3µC is placed at the origin. A negative charge of −1µC is placed at 10 cm along the negative
x-axis. A particle of mass 4.2 g and of negative charge Qo is released from rest very far on the positive x-axis (from
infinity). It has a speed of 10 m/s when it reaches a point P located 20 cm on the right of the origin on the positive
x-axis. What is the magnitude of Qo ? (Hint: think energy conservation.)
(1) 2µC
(2) 4µC
(3) 3µC
(4) 1µC
(5) 7µC
5. An electron is moving at 107 m/s when it enters a region of a uniform electric field E, pointing along the direction of
the electron’s velocity. How strong does the electric field E have to be [V/m] to stop the electron over a distance of
5 cm?
(1) 5.7 × 103
(2) 2.8 × 103
(3) 1.1 × 104
(4) 1.4 × 103
(5) 2.3 × 104
6. Two capacitors C1 = 4µF and C2 = 2µF are connected in series and are charged with a 100 V battery. The two
capacitors are then disconnected from the battery and from each other. Next they are reconnected (without being
discharged) positive plate to positive plate and negative plate to negative plate. What is the resulting energy [in J]
that is stored in the combined capacitors. (Note that in this process energy is NOT conserved).
(1) 5.9 × 10−3
(2) 1.2 × 10−2
(3) 5.4 × 10−1
(4) 2.4 × 10−2
(5) 1.5 × 10−3
7. Three equal charges, each +5µC are arranged at the corners of an equilateral triangle of side length 10 cm. The
electrostatic energy of one of these charges [in J] is
(1) 4.5
(2) −4.5
(3) 2.3
(4) 45
(5) −2.3
8. Consider the combination of capacitors shown in the figure. If the
charge on the 24µF capacitor is 16µC, what is the voltage drop
across the 4µF capacitor.
(1) 2.7 V
(2) 3.9 V
(3) 5.6 V
(4) 6.0 V
(5) 2.0 V
(4) 0.48
(5) 0.27
9. A set of capacitors is connected as in the figure. C1 = 5µF,
C2 = 10µF and C3 = 2µF. A battery that provides 500 V is
now connected to points a and b. How much energy [in J] is stored
in the set?
(1) 0.76
(2) 0.81
(3) 0.93
10. Three very large planar parallel nonconducting sheets of charge
are placed 0.5 m apart. They carry respective surface charges σ1 =
−5nC/m2 , σ2 = +3nC/m2 and σ3 = −5nC/m2 . A charge Qo =
+18×10−3 C is moved from point A to point B, a distance of 0.25 m
apart. Points A and B lie between sheets 2 and 3. What is the
change in potential energy [in J] of charge Qo , PE (B) – PE (A)?
(1) −0.76
(2) +0.76
(3) +3.25
σ3
B
A
0.25 m
0.5 m
σ2
0.5 m
σ1
(4) −0.25
(5) −3.25
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11. Two small spheres, each of mass 0.2g are suspended as pendula
by light nonconducting strings from a common point as shown in
the figure. The spheres are given the same negative electric charge
−Q of magnitude 3 nC. Each pendulum comes to rest at an angle
of 5◦ with the vertical. Both charges Q are now changed, and the
new equilibrium angle is 10◦ . The magnitudes of the new charges
are
(1) 8.5 nC
(2) 25 nC
(3) 5.7 nC
(4) 2.8 nC
(5) 4.3 nC
12. Three concentric conducting shells carry successive net charges Q1 = −5µC, Q2 = −5µC and Q3 = +10µC, and have
radii 0.5 m, 0.75 m and 1.0 m. Find the surface charge on the inner surface of the outer shell [in µC/m2 ].
(1) +0.8
(2) 0
(3) −1.0
(4) −0.4
13. Six charges of equal magnitudes Q = 1µC are located on the vertices of a regular hexagon. Opposing charges have opposite signs.
The sides of the hexagon are a = 10 cm. A charge Qo = 2µC is now
brought from infinity to the center of the hexagon. The change in
potential energy of Qo is
(5) +0.4
+Q
a
+Q
Q
Q
(1) none of these
(2) 1.08 J
(3) −1.08 J
+Q
(4) 0.54 J
Q
(5) −0.54 J
14. Your neighbors are too lazy to turn on and off their porchlights every day so they let them burn continuously. The
2 bulbs that are in their porchlights are rated 150 W each. How much does it cost them on a monthly basis to have
their porchlights on 24 hours a day, if they get charged 12/c a kW-hr?
(1) $26
(2) $13
(3) $6.5
(4) $3.3
(5) $1.6
15. What is the resistance of a light bulb rated for 60 W at 120 V?
(1) 240 ohm
(2) 0.5 ohm
(3) 30 ohm
(4) 7200 ohm
(5) 2 ohm