# Exam1, 1402, Summer II, 2008

advertisement ```Review for the 3rd exam, 2426, Chpt. 29 – 32. Lianxi Ma
First part: multiple choice.
1.
(c) (see figure below) A circular loop of wire is in a region of spatially uniform magnetic field. The
magnetic field is directed into the plane of the figure. If the magnetic field magnitude is constant,
A. the induced emf is clockwise.
B. the induced emf is counterclockwise.
C. the induced emf is zero.
D. The answer depends on the strength of
the field.
2.
(a) (see figure above) A circular loop of wire is in a region of spatially uniform magnetic field.
The magnetic field is directed into the plane of the figure. If the magnetic field magnitude is
decreasing,
A. the induced emf is clockwise.
B. the induced emf is counterclockwise.
C. the induced emf is zero.
D. The answer depends on the strength of the field.
3.
(a) A circular loop of wire is placed next to a long straight wire. The current I in the long straight
wire is increasing. What current does this induce in the circular loop?
A. a clockwise current
B. a counterclockwise current
C. zero current
D. not enough information given to
decide
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4.
(a) A flexible loop of wire lies in a uniform magnetic field of magnitude B directed into the plane of
the picture. The loop is pulled as shown, reducing its area. The induced current
A. flows downward through resistor R and
is proportional to B.
B. flows upward through resistor R and is
proportional to B.
C. flows downward through resistor R and
is proportional to B2.
D. flows upward through resistor R and is
proportional to B2.
E. none of the above
5.
(e) The rectangular loop of wire is being moved to the right at constant velocity. A constant current
I flows in the long straight wire in the direction shown. The current induced in the loop is
A. clockwise and proportional to I.
B. counterclockwise and proportional
to I.
C. clockwise and proportional to I2.
D. counterclockwise and proportional
to I2.
E. zero.
6.
(a) The loop of wire is being moved to the right at constant velocity. A constant current I flows in
the long straight wire in the direction shown. The current induced in the loop is
A. clockwise and proportional to I.
B. counterclockwise and proportional to I.
C. clockwise and proportional to I2.
D. counterclockwise and proportional to I2.
E. zero.
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7.
(b) (see figure above) The rectangular loop of wire is being moved to the right at constant
velocity. A constant current I flows in the long wire in the direction shown. What are the directions
of the magnetic forces on the left-hand (L) and right-hand (R) sides of the loop?
A. L: to the left; R: to the left
B. L: to the left; R: to the right
C. L: to the right; R: to the left
D. L: to the right; R: to the right
8.
(a) The drawing shows the uniform magnetic field inside a long, straight solenoid. The field is
directed into the plane of the drawing, and is increasing. What is the direction of the electric force
on a positive point charge placed at point a?
A. to the left
B. to the right
C. straight up
D. straight down
E. misleading question — the electric force at
this point is zero
9.
(c) (see figure above) The drawing shows the uniform magnetic field inside a long, straight
solenoid. The field is directed into the plane of the drawing, and is increasing. What is the direction
of the electric force on a positive point charge placed at point b?
A. to the left
B. to the right
C. straight up
D. straight down
E. misleading question — the electric force at this point is zero
10.
(e) Continued from 9. What is the direction of the electric force on a positive point charge placed at
point c (at the center of the solenoid)?
A. to the left
B. to the right
C. straight up
D. straight down
E. misleading question — the electric force at this point is zero
11.
(c) A small, circular ring of wire (shown in blue) is inside a larger loop of wire that carries a current
I as shown. The small ring and the larger loop both lie in the same plane. If I increases, the current
that flows in the small ring
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A. is clockwise and caused by selfinductance.
B. is counterclockwise and caused by selfinductance.
C. is clockwise and caused by mutual
inductance.
D. is counterclockwise and caused by
mutual inductance.
12.
(a) A current i flows through an inductor L in the direction from point b toward point a. There is
zero resistance in the wires of the inductor. If the current is decreasing,
A. the potential is greater at point a than at point b.
B. the potential is less at point a than at point b.
C. the answer depends on the magnitude of di/dt compared to the magnitude of i.
D. The answer depends on the value of the inductance L.
E. both C. and D. are correct.
13.
(c) A steady current flows through an inductor. If the current is doubled while the inductance
remains constant, the amount of energy stored in the inductor
A. increases by a factor of 2 .
B. increases by a factor of 2.
C. increases by a factor of 4.
D. increases by a factor that depends on the geometry of the inductor.
E. none of the above
14.
(e) An inductance L and a resistance R are connected to a source of emf as shown. When switch S1
is closed, a current begins to flow. The final value of the current is
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A. directly proportional to RL.
B. directly proportional to R/L.
C. directly proportional to L/R.
D. directly proportional to 1/(RL).
E. independent of L.
15.
(c) Continued from problem 14. When switch S1 is closed, a current begins to flow. The time
required for the current to reach one-half its final value is
A. directly proportional to RL.
B. directly proportional to R/L.
C. directly proportional to L/R.
D. directly proportional to 1/(RL).
E. independent of L.
16.
(c) Continued from 14. Initially switch S1 is closed, switch S2 is open, and current flows through L
and R. When S2 is closed, the rate at which this current decreases
A. remains constant.
B. increases with time.
C. decreases with time.
D. not enough information given to decide
17.
(b) An inductor (inductance L) and a capacitor (capacitance C) are connected as shown. If the
values of both L and C are doubled, what happens to the time required for the capacitor charge to
oscillate through a complete cycle?
A. It becomes 4 times longer.
B. It becomes twice as long.
C. It is unchanged.
D. It becomes 1/2 as long.
E. It becomes 1/4 as long.
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18.
(d) Continued from problem 17. At any instant, the potential difference between the capacitor plates
is
A. proportional to q.
C. proportional to d2q/dt2.
E. all of A, B, and C.
19.
B. proportional to dq/dt.
D. both A and C.
(a) A resistor is connected across an ac source as shown. For this circuit, what is the relationship
between the instantaneous current i through the resistor and the instantaneous voltage vab across the
resistor?
A. i is maximum at the same time as vab
B. i is maximum one-quarter cycle before vab
C. i is maximum one-quarter cycle after vab
D. not enough information given to decide
20.
(c) An inductor is connected across an ac source as shown. For this circuit, what is the relationship
between the instantaneous current i through the inductor and the instantaneous voltage vab across
the inductor?
A. i is maximum at the same time as vab
B. i is maximum one-quarter cycle before vab
C. i is maximum one-quarter cycle after vab
D. not enough information given to decide
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21.
(c) An L-R-C series circuit as shown is operating at its resonant frequency. At this frequency, how
are the values of the capacitive reactance XC, the inductive reactance XL, and the resistance R
related to each other?
A. XL = R; XC can have any value.
B. XC = R; XL can have any value.
C. XC = XL; R can have any value.
D. XC = XL = R.
E. none of the above
22.
(b) In an L-R-C series circuit, the current has a very small amplitude if the ac source oscillates at a
very high frequency due to the large impedance. Which circuit element causes this behavior?
A. the resistor R
B. the inductor L
C. the capacitor C
D. misleading question — the current actually has a very large amplitude if the frequency
is very high
23.
(b) In an L-R-C series circuit, suppose that the angular frequency of the ac source equals the
resonance angular frequency. In this case, the circuit impedance
A. is maximum.
B. is minimum, but not zero.
C. is zero.
D. is neither a maximum nor a minimum.
E. not enough information give to decide
24.
(b) In a transformer, there are more turns in the secondary than in the primary. In this situation,
the voltage amplitude is
A. greater in the primary than in the secondary.
B. smaller in the primary than in the secondary.
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C. the same in the primary and in the secondary.
D. not enough information given to decide
25.
(e) In a vacuum, red light has a wavelength of 700 nm and violet light has a wavelength of 400
nm. This means that in a vacuum, red light
A. has higher frequency and moves faster than violet light.
B. has higher frequency and moves slower than violet light.
C. has lower frequency and moves faster than violet light.
D. has lower frequency and moves slower than violet light.
E. none of the above
26.
(b) A sinusoidal electromagnetic wave in a vacuum is propagating in the positive z-direction. At a
certain point in the wave at a certain instant in time, the electric field points in the negative xdirection. At the same point and at the same instant, the magnetic field points in the
A. positive y-direction .
C. positive z-direction.
E. none of the above
27.
B. negative y-direction.
D. negative z-direction.
(b) In a sinusoidal electromagnetic wave in a vacuum, the magnetic energy density
A. is the same at all points in the wave.
B. is maximum where the electric field has its greatest value.
C. is maximum where the electric field is zero.
D. none of the above
28.
(d) The drawing shows a sinusoidal electromagnetic wave in a vacuum at one instant of time at
points between x = 0 and x = . At this instant, at which values of x does the instantaneous
Poynting vector have its maximum magnitude?
A. x = 0 and x =  only
B. x = /4 and x = 3/4 only
C. x = /2 only
D. x = 0, x = /2, and x = 
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Part II, Free response problems.
1. A circular loop of flexible iron wire has an initial circumference of 165 cm, but its circumference is
decreasing at a constant rate of 15.0 cm/s due to a tangential pull on the wire. The loop is in a
constant uniform magnetic field of magnitude 0.800 T, which is oriented perpendicular to the plane of
the loop. Assume that you are facing the loop and that the magnetic field points into the loop. Find the
emf induced in the loop after exactly time 9.00 s has passed since the circumference of the loop
started to decrease. (5.7310-3 V; clockwise).
2. A conducting disk with radius R = 0.5 m, lies in the xy-plane and rotates with constant
angular velocity  = 120 rpm about the z-axis. The disk is in a uniform, constant B = 0.5 T
field parallel to the z-axis. (This is actually the Faraday disk dynamo, see our example in
lecture note/textbook) Find the induced emf between the center and the rim of the disk.
(0.785 V, rim’s potential is higher than that of center)
3. Consider the L-R circuit shown in the figure. Initially, the switch connects a resistor of resistance R
and an inductor to a battery, and a current I0flows through the circuit. At time t = 0, the switch is
thrown open, removing the battery from the circuit. Suppose you measure that the current decays to
I1at time t1. (a) Determine the time constant of the circuit. (b) What is the inductance L of the inductor?
 
t1
Rt1
; L
ln  I1 / I 0 
ln  I1 / I 0 
4. A 7.50-nF capacitor is charged up to 12.0 V, then disconnected from the power supply and
connected in series through a coil. The period of oscillation of the circuit is then measured to
be 8.6010-5 s. calculate: (a) the inductance of the coil; (b) the maximum charge on the
capacitor; (c) total energy of the circuit; (d) the maximum current of the circuit.(25.0 mH,
910-8 C, 5.4010-7 J, 6.57 mA)
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5. A toroidal solenoid shown below. Suppose N = 200, A = 5 cm2, r = 0.1 m, compute L. If the current
increases from 0 to 6.0 A in 3.0 s, fin the induced emf. (40 H, 80 V)
6. In the series RLC circuit, suppose R = 300 , L = 60 mH, C = 0.50 F, total voltage amplitude is
V = 50 V, and the AC source  = 10,000 rad/s. Find the Z, amplitude of I, , and the voltage
total
amplitude across each circuit element. (500 , 0.1 A, 53, 30V, 60 V, 20 V).
7. For the nonsinusoidal wave, suppose that E = 100 V/m (rms value). Find the Brms, the energy density,
and the average S. (3.3310-7 T, 8.8510-8 J/m3, 26.5 W/m2)
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