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Instructor(s): Reitze/Kumar
PHYSICS DEPARTMENT
Exam 1
PHY2054
Name (print, last first):
September 29, 2010
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 lines 76–80 on the answer sheet 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.
(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.
Useful Constants:
9
2
2
ke = 8.99 × 10 Nm /C
²0 = 8.85 × 10−12 C2 /(Nm2 )
V=volt
N=newton
−19
−31
electron charge = −1.6 × 10 C electron mass = 9.11 × 10 kg
J=joule
m=Meter
−3
−6
−9
−12
“milli”=10
“micro”=10
n=“nano”=10
“pico”=10
C=coulomb g = 9.8 m/s2
1. At what distance (in m) from a 0.9 Coulomb point charge is the magnitude of the electric field produced by the charge
equal to 899 N/C?
(1) 3,000
(2) 9,000
(3) 300
(4) 900
(5) 30
2. A 1 gram particle with a charge of 1 milliC starts from rest in a uniform electric field with magnitude, E = 10 N/C.
How far will the particle move (in m) in 2 seconds?
(1) 20
(2) 10
(3) 40
(4) 5
(5) 30
3. Two point charges lie on the x-axis. Charge Q1 = +7µC is located at x = 0 and charge Q2 = −18µC is located at
x = 25 cm. Find the point on the x axis (in cm) where the net electric field is zero.
(1) −41.4
(2) 9.6
(3) −14.2
(4) 20.0
4. Near the surface of the Earth, a small plastic ball with mass M = 5 grams is
suspended by a 20 cm long thin string in a uniform electric field with magnitude
E = 1, 000 N/C as shown in the figure. If the ball makes an angle θ = 15◦
with the vertical, what is the net charge on the ball (in µC)?
(1)
(2)
(3)
(4)
(5)
13.1
5.3
49.0
9.2
10.6
(5) −20.0
θ
Electric Field
M
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5. Two identical point charges +Q are located on the y-axis at y = d/2 and
y = −d/2 as shown in the figure. What is the magnitude of the electric field
on the x-axis a distance x = d/2 from the origin?
(1)
(2)
(3)
(4)
(5)
2.83ke Q/d2
1.41ke Q/d2
0.71ke Q/d2
5.6ke Q/d2
4ke Q/d2
y-axis
+Q
x
d
x-axis
+Q
6. If the magnitude of the electric field at the surface of an isolated solid spherical conducting ball is 0.1 V/m and the
electric potential of the ball is 899 Volts, what is the capacitance C of the ball (in µF)?
(1) 1
(2) 10
(3) 8.99
(4) 89.9
(5) 0.1
7. A uniform electric field of intensity 0.318 N/C is pointing along the x-axis.
What is the magnitude of the electric flux (in Nm2 /C) through a circular
plane with radius R = 2 m if the normal of the circle is in the xy-plane and
makes an angle of 60◦ with the x-axis as shown in the figure?
y-axis
Normal
60o
Electric Field
x-axis
Circle
(1) 2
(2) 4
(3) 1
(4) 0.5
8. Consider the two isolated capacitors shown in the figure. Capacitor #1 has
capacitance C1 = 1µF and capacitor #2 has capacitance C2 = 2µF. Suppose
that you have a total charge Qtot = 30µC that must be stored on the two
capacitors, with Q1 placed on C1 and Q2 placed on C2 such that Q1 + Q2 =
Qtot . If you place Qtot /2 on each of the two capacitors (i.e., Q1 = 15µC,
Q2 = 15µC), how much total stored energy, Utot = U1 + U2 , is there on the
two capacitors (in µJ)?
(1) 168.75
(2) 450
(3) 150
(5) 3
C1
(4) 84.38
C2
(5) 300
9. In the previous problem, how much electric charge, Q1 and Q2 (in µC), should you place on each of the two capacitors
to minimize the total amount of stored energy, Utot = U1 + U2 ?
(1) Q1 = 10, Q2 = 20
(2) Q1 = 20, Q2 = 10
(3) Q1 = 15, Q2 = 15
(4) Q1 = 5, Q2 = 25
10. Four point charges form a square and lie on a circle of radius R. Two of the
charges have charge +Q and two have charge −Q as shown in the figure. What
is the electric potential, V , at the center of the circle? (Take V = 0 at infinity
as the reference point.)
(2) 4ke Q/R
(3) 2ke Q/R
(4) 2.81ke Q/R
-Q
+Q
R
-Q
(1) zero
(5) Q1 = 25, Q2 = 5
+Q
(5) 0.5ke Q/R
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11. Four point charges form a square and lie on a circle of radius R. Two of the
charges have charge +Q and two have charge −Q as shown in the figure. What
is the electric potential energy, PE, of this charge configuration?
-Q
+Q
R
-Q
(1) −1.83ke Q2 /R
(2) −0.91ke Q2 /R
(3) 0.91ke Q2 /R
+Q
(4) 1.41ke Q2 /R
(5) zero
12. In the previous problem, what is the minimum amount of work that must be done (against the electric force) to move
one of the +Q charges to infinity?
(1) 0.91ke Q2 /R
(2) −0.91ke Q2 /R
(3) −1.83ke Q2 /R
(4) 1.41ke Q2 /R
(5) zero
13. When a 12 Volt battery is connected to the plates of a capacitor, it stores a charge of 24µC. If the same capacitor is
connected to a 15 Volt battery, what charge (in µC) is stored?
(1) 30
(2) 15
(3) 2
(4) 24
(5) 19.2
14. If a current of 1.6µA exists in a metal wire, how many electrons flow past a given cross section of the wire in 1
microsecond?
(1) 10 million
(2) 1 million
(3) 100 million
(4) 10,000
(5) 100,000
15. A high-voltage transmission line with a resistance of 0.1Ω/km carries a current of 1,000 A. The line is at a potential
of 800 kV at the power station and carries the current to a city located 200 km from the station. What fraction of the
transmitted power arrives at the city?
(1) 97.5%
(2) 95%
(3) 99%
(4) 90%
(5) 75%
16. A battery with an internal resistance of 0.5Ω is connected to a 10Ω resistor. If the voltage across the battery (the
terminal voltage) is 20 Volts, what is the emf of the battery (in Volts)?
(1) 21
(2) 20
(3) 19
(4) 24
17. In the electric circuit shown, C1 = 4µF, C2 = 8µF, and C3 = 3µF. The amount
of charge stored in capacitor CX is exactly the same as the charge stored in
C2 . What is the capacitance CX (in µF) ?
(1) 24
(2) 15
(3) 9
(2) 1.5
(3) 6
(4) 9
C1
CX
C2
C3
∆V
(4) 4
18. Two identical point charges each with a mass of 1 gram and a charge of 1µC
are released from rest 1 meter apart. They repel each other and fly apart as
shown in the figure. What is their speed (in m/s) when they are 2 meters
apart?
(1) 2.1
(5) 22
(5) 8
v
v
(5) 3
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19. Two identical small insulated conducting spheres, whose centers are 18.9 cm apart, carry charges Q1 = −100µC and
Q2 = −200µC, respectively. The spheres are kept insulated, but are then brought into mutual contact and then returned
to their original positions. How much does the potential energy (in J) of the two spheres change from the initial to the
final configuration (i.e., P Ef − P Ei )?
(1) 118.9
(2) 96.1
(3) 81.4
(4) −118.9
(5) −96.1
20. A copper cable with resistivity ρ = 1.7 × 10−8 Ω/m is designed to carry a current of 300 Amps with a power loss of 2.0
W/m. What is the required radius of this cable (in cm)?
(1) 1.56
(2) 1.41
(3) 0.83
(4) 2.35
(5) 0.66
THE FOLLOWING QUESTIONS, NUMBERED IN THE ORDER OF THEIR APPEARANCE ON THE ABOVE
LIST, HAVE BEEN FLAGGED AS CONTINUATION QUESTIONS: 9 12