Download A capacitor consists of two charged disks of radius

PHYS 272 Spring 2012
Machine Answer Sheet:
Using a pencil, fill in Last Name, First Name, & Middle Initial, plus your 10-digit Purdue
University ID number. Enter Instructor (Hirsch), Course (PHYS 272/272H), Date
(12/10/07), and Test (3). You must include your Signature.
1
Problem 1
The figure below shows the electric potential as a function of distance in a region of
space. What is the change in the electric potential energy in moving a charge Q = -[3] nC
from x = 5 meters to x = 18 meters?
V(x)
6V
5
10
18
X(m)
-5V
-10 V
A. -11 Q x 10-9 J
B. 11 Q x 10-9 J
C. -13 Q x 10-9 J
D. 13 Q x 10-9 J
E. 19 Q x 10-9 J
Problem 2
A capacitor with plates separated by [d] 2 mm has one plate at a potential of 300 Volts
and its other plate at a potential of [V2] 250 Volts. What is the magnitude of the electric
field between the plates of the capacitor?
A.
B.
C.
D.
E.
(300-V2)x103 /[d] N/C
2(300-V2)/d N/C
(300-V2) N/C
(300+V2)x103 /[d]N/C
(300+V2)/[d] N/C
2
Problem 3
A fully charged 100 µF (=10-4 F) capacitor has a potential difference across it of 9 Volts.
It is then connected to a resistor of [10] Ω. How long will it take for the current through
the resistor to decrease to 1/10 of its initial value? [Recall that Q(t) = Cemf [1- e
A.
B.
C.
D.
-t
RC
]]
2.3*[R] x 10-4 seconds
[R]/2.3x10-4 seconds
[R] x 10-4 seconds
1/[R] x10-4 seconds
Problem 4
A particular alnico (aluminum, cobalt, nickel, and iron bar magnet (magnet A) has a mass
of 10 grams. It produces a magnetic field of magnitude [B] 6 x 10-5 T at a location of [d]
0.19 m from the center of the magnet, on the axis of the magnet. If you replaced this
magnet with a magnet made of the same material but with a mass of 50 grams (magnet
B), approximately what would be the magnetic field at a location [2d] 0.38 m from the
center of the magnet, on the axis of the magnet?
A.
B.
C.
D.
E.
5[B]/8 T
8[B]/5 T
5[B] T
[B]/8 T
5[B]/2 T
Problem 5
A capacitor consists of two charged disks of radius R separated by a distance s, where
R>>s. The magnitude of the charge on each disk is Q. If Q = [43] C, R = [4.0] m, s =
1.7 mm, s1 = 1.5 mm, and s2 = 0.7 mm, what is the value of V = VC - VA?
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A.
B.
C.
D.
E.
[Q][s1]/(0R2) Volts
-[Q][s1]/ (0R2) Volts
0 Volts
–[Q][s]/ (0R2) Volts
[Q][s]/ (0R2) Volts
Problem 6
Point charges Q1 = [6 nC], Q2 = [-5 nC], Q3 = [8 nC] and Q4 = [-7 nC] are fixed in
position in a square pattern that has sides of length L = 4 mm. How much work must an
external agent do in order to bring a charge q = 5 nC from far away to the square’s
center?
4
A. Wext =
Q1
Q2
Q4
Q3
1 q 2
(Q1 + Q2 + Q3 + Q4 ) J
4pe0 L
1 q 2
(Q1 + Q2 + Q3 + Q4 ) J
4pe0 L
1 éq 2
1æ
Q Q Q Q öù
C. Wext =
ê
(Q1 +Q2 +Q3 +Q4 ) + çQ1Q2 +Q1Q4 +Q2Q3 +Q3Q4 + 1 3 + 2 4 ÷ú
4 pe 0 ë L
Lè
2
2 øû
B. Wext = -
D. Wext =
1 é q 2
1æ
Q Q Q Q öù
ê(Q1 +Q2 +Q3 +Q4 ) + çQ1Q2 +Q1Q4 +Q2Q3 +Q3Q4 + 1 3 + 2 4 ÷ú
4 pe 0 ë L
Lè
2
2 øû
Problem 7
Two large conducting disks form a capacitor. The radius, R = 1 cm, of each disk is much
larger than the separation between disks, s = .05 cm. Of the answers below, which is the
best estimate of force exerted on the right disk by the left disk when the potential
difference across the capacitor is [100] Volts?
[Formula below has R and s in cm]
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A. 1.39 ´10 -11
R2 2
V N
s2
B. 2.78 ´10 -11
R2 2
V N
s2
C. 2.78´10-11
R2
VN
s3
D. 2.78 ´10 -11
E. 0 N
R2
VN
s2
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Problem 8
Two identical concentric conducting loops are arranged as shown in the figure below.
One loop has a steady current flowing through it (provided by the power supply shown.)
Will the two loops briefly attract or repel each other when the power is turned off?
A.
B.
C.
D.
They will attract each other.
They will repel each other.
They will neither attract nor repel each other.
The answer depends on the direction current was flowing in loop 1.
Problem 9
Consider the circuit shown below. If you were to unscrew bulb B from its socket
(effectively removing it from the circuit), bulb A would
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A. Get dimmer
B. Get brighter
C. Remain the same
D. Go out
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Problem 10
Just prior to t = 0, the capacitor ( C =1´10-3 F ) in the circuit below has a charge Q0 = [4]
C. The inductor has inductance L = 3x10-4 H. At t=0, a switch (not shown) is closed,
allowing current to flow around the circuit. What is the magnitude of the current when
1
the charge on the capacitor has fallen to 0.5 C? [Recall that Q(t) = Q0 cos(
t) ]
LC
A. i =
Q0
Q2
(1- 2 ) Amperes
Q0
LC
Q0
Q2
B. i =
(1- 2 ) Amperes
LC
Q0
Q0
Q2
( 02 -1) Amperes
LC Q
Q
D. i = 0 Amperes
LC
Q
E. i =
Amperes
LC
C. i =
Problem 11 An ion whose charge is q = +2e and whose mass is M enters a velocity
selector, a region of space in which there is a magnetic field directed out of the page and
an electric field perpendicular to the magnetic field as shown in the figure. If B = [0.3] T,
what electric field strength will allow only those ions traveling with speed 0.01 c (= 3 x
106 m/s) through the small slit.
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A.
B.
C.
D.
E.
B*3 x 106 N/C
B/(3 x 106) N/C
2*B*3 x 106 N/C
2*B/(3 x 106) N/C
Not enough information
Problem 12 You are presented with a length of wire L and told its resistance is R. If this
wire is stretched until its length is 2L, its new resistance R’ would be [Hint: Assume the
density of the wire remains constant.]
A.
B.
C.
D.
E.
4R
2R
R
8R
R/2
Problem 13 A circular wire loop moving at constant velocity enters a long region of
uniform magnetic field B that is perpendicular to the plane determined by the loop.
Which one of the graphs best describes the emf  in the loop as a function of time t?
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A.
B.
C.
D.
E.
A
B
C
D
E
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Problem 14 A proton enters a magnetic field and follows trajectory 2. An alpha particle
(twice the charge and 4 times the mass) enters the same magnetic field in the same way
and with the same velocity as the proton. Which of the following is the correct trajectory
for the alpha?
A.
B.
C.
D.
E.
3
2
1
4
5
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Problem 15 The following are two-dimensional cross sections through 4 spherical shells
and one cube. Rank in order, from largest to smallest, the electric fluxes a to b through
surfaces a to e.
A.
B.
C.
D.
E.
Φb = Φe > Φa = Φc = Φd
Φa > Φc > Φb > Φd > Φe
Φe > Φd > Φb > Φc > Φa
Φb > Φa > Φc > Φe > Φd
Φd = Φe > Φc > Φa = Φb
Problem 16 A positive charge undergoes a brief acceleration at time t = 0 in the –y
direction. At the instant shown, the charge lies along the x-axis. Detectors are arranged in
a circle of radius R in the x-y plane so that at time t = R/c the radiation reaches the
detectors. At what angle as measured from the positive x-axis will the intensity of the
radiated field as measured by the detectors be ½ of its maximum value (for the same
distance from the charge)?
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y
x
A.
B.
C.
D.
E.
45, 135, 225, 315 degrees from the x-axis
0 and 180 degrees from the x-axis
90 and 270 degrees
60, 120, 240, 300
30, 150, 210, 330
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Problem 17
A wire carrying a current of circular cross section I has two segments which have equal
diameters. If the conductivities for the two segments have the ratio σ1:σ2=2:1, what is the
ratio E1:E2 of the electric field strengths in the two segments of the wire.
A.
B.
C.
D.
E.
E1/E2 = 1/2
E1/E2 = 1/4
E1/E2 = 1/1
E1/E2 = 2/1
E1/E2 = 4/1
Problem 18 A thick wire of radius R carries a current I1. The magnetic field inside the
wire a distance r from the center of the wire where r < R is
m0 I1r
2p R 2
mIR
B. B = 0 1 2
2p r
m 0 I1
C. B =
2p R
A. B =
15
D. B =
m 0 I1
2p r
Problem 19 A long straight wire suspended in the air carries a conventional current of
[8.2] amperes in the –x direction as shown in the figure below. The wire runs along the xaxis. At a particular instant, an electron at location <0, -0.003, 0> m has a velocity of <1.5 x 105, -1.8 x 105, 0> m/s. The magnetic force on the electron due to the current in the
wire is
A. <1.92I,-1.6I,0 > ×10-18 N
B. <1.92I,1.6I,0 > ×10-18 N
C. < -1.92I,1.6I,0 > ×10-18 N
D. < -1.92I,-1.6I,0 > ×10-18 N
Problem 20 Which figure below correctly displays the polarization of an initially
uncharged plastic sphere by an electric field that points to the left?
A. B
B. A
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C.
D.
E.
F.
C
D
E
F
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