Fall 2005 Physics 102 Hour Exam 2(29 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 131. The exam period was 90 minutes; the mean score was 94.5; the median was 97. Click here to see page1 page2 of the formula sheet that came with the exam.

QUESTION 1***

This and the next question pertain to the following situation.

In a region of space there is a constant magnetic field as shown in the shaded part of the figure below.  A square loop of side L = 0.1 m and resistance R = 12 Ω is moved at constant velocity of 0.1 m/s in the direction indicated by the arrow.  The magnetic field extends for a length L = 0.1 m in the direction of motion. In the figure below, which of the waveforms best describes the current in the loop as a function of time?

(a)
(b)
(c)
(d)
(e)

QUESTION 2*

In the previous situation, if the resistance of the loop is R = 12 Ω and B0= 0.6 T, what is the maximum current I in the loop?

(a)   I = 0.1 mA
(b)   I = 2 mA
(c)   I = 0.5 mA
(d)   I = 1 A
(e)   I = 1 mA

QUESTION 3**

A current I = 3 A is flowing in the conducting loop as shown below.  A constant magnetic field B = 0.7 T is in the direction to the right in the shaded regions in the figure.  The loop can rotate along an axis in the y direction as shown.  The size of the loop and the location with respect to the regions of constant magnetic field are shown in the figure.

What is the torque on the loop at the position shown in the figure (torque = F r sinα)?

(a)   torque = 0.084 Nm
(b)   torque = 3.5 Nm
(c)   torque = 0 Nm
(d)   torque = 0.21 Nm
(e)   torque = 0.168 Nm

QUESTION 4*

This and the next two questions pertain to the following situation.

In a region of space of width L = 0.1 m there is a magnetic field B = 0.25 T pointing into the page as shown in the figure.  A 1 mg particle with speed v and charge Q = -2 mC enters the region of the magnetic field along the line indicated in the figure.  Ignore gravity in this problem. (Note that Q is negative.)

What is the direction of the force on the particle when the particle enters the region of the magnetic field?

(a)   +z (up out of the page)
(b)   -z (down into the page
(c)   +y
(d)   -y
(e)   +x

QUESTION 5**

For the configuration of magnetic field and particle of the previous question, what is the minimum speed that the particle must have when it enters the region of the magnetic field in order to escape to the right of the region occupied by the magnetic field?

(a)   v = 105 m/s
(b)   v = 50 m/s
(c)   v = 5000 m/s
(d)   v = 250 m/s
(e)   v = 2000 m/s

QUESTION 6*

Assuming that v is the answer to the previous question, what is the value of the speed when the particle escapes to the right of the region occupied by the magnetic field?

(a)   same as v
(b)   greater than v
(c)   less than v

QUESTION 7**

This and the next question pertain to the following situation.

A circular loop of radius r = 5 cm and resistance R = 0.10 Ω is in a region where there is a uniform magnetic field in the direction shown in the figure that increases linearly with time according to the expression

B(t) = B0 t / τ
with B0 = 0.5 T and t = 100 s. (The loop is stationary.)

What is the direction of the current in the loop (choose between a and b arrows as indicated in the figure [front view])?

(a)
(b)

QUESTION 8***

For the situation described in the previous question, what is the magnitude of the induced current in the loop?

(a)   I = 0
(b)   I = 0.34 mA
(c)   I = 0.39 mA
(d)   I = 0.2 mA
(e)   I = 3.4A

QUESTION 9*

This and the next two questions pertain to the following situation.

An ideal transformer with 5 turns on the primary and 10 turns on the secondary is shown in the figure.  A sinusoidal voltage source having V(t) = 10 sin(ωt) [in volts] is connected across the primary and a 1 Ω resistor is connected across the secondary. ω = 100 rad/s.

What is the maximum value of the voltage in the secondary circuit?

(a)   5 volts
(b)   10 volts
(c)   20 volts

QUESTION 10**

What is the maximum value of the current in the primary circuit (not the secondary)?

(a)   2.0 Amp
(b)   5.0 Amp
(c)   10.0 Amp
(d)   20.0 Amp
(e)   40.0 Amp

QUESTION 11**

If the frequency ω is doubled, what would happen to the rms voltage in the secondary circuit?

(a)   doubles
(b)   halves
(c)   stays the same

QUESTION 12*

This and the next two questions pertain to the following situation.

An alternating voltage source of 10 volts (rms) at 60 Hz is applied to a circuit depicted below. The capacitor C = 100 μF. What is the rms value of the current through the resistor R?

(a)   0
(b)   0.26 A
(c)   0.46 A
(d)   0.65 A
(e)   2.15 A

QUESTION 13*

What is the phase angle between ε (the voltage across the generator) and VR (the voltage across the resistor)?

(a)   50°
(b)   62°
(c)   72°
(d)   42°
(e)   32°

QUESTION 14*

What is the phase angle between VR (the voltage across the resistor) and VC (the voltage across the capacitor C)?

(a)   zero
(b)   90°
(c)   180°

QUESTION 15*

This and the next two questions pertain to the following situation.

A coil of 22 turns and length 40 cm is connected to a voltmeter. A time-dependent magnetic field is generated by a moving magnet nearby.

The average magnetic flux inside the coil as a function of time
for (t < 0.1s) is given by the expression

Φ(t)  = (2 - t / 0.05s) 10-4 T m2

(See figure below.)

What is the induced EMF of the coil
for 0 < t < 0.1?

(a)   0.33 volts
(b)   0.22 volts
(c)   0.11 volts
(d)   0.044 volts
(e)   0.022 volts

QUESTION 16***

For t > 0.1s, the average magnetic flux inside the coil is given by a sinusoidal expression Φ(t)  = (10-4 T m2) sin ωt, where ω = 180 s-1. What is the maximum value of the induced EMF of the coil?

(a)   0.132 volts
(b)   0.248 volts
(c)   0.396 volts
(d)   2.48 volts
(e)   1.32 volts

QUESTION 17*

The condition remains the same as in problem above.  If the number of turns of coil is doubled, while keeping the length and diameter the same, what would be the maximum value of the induced EMF of the coil?

(a)   the same
(b)   twice as big
(c)   half

QUESTION 18*

This and the next two questions pertain to this series RLC circuit:

What is the resonant frequency of this RLC circuit?

(a)   312.5 radians/sec = 49.7 Hz
(b)   158.1 radians/sec = 25.2 Hz
(c)   17.7 radians/sec = 2.8 Hz

QUESTION 19**

If the frequency of the AC source is set to the circuit's resonant frequency, the current provided by the AC source will be minimized.

(T)   True
(F)   False

QUESTION 20*

When driven at its resonant frequency, the maximum current flowing in the circuit is

(a)   I = 0
(b)   I = 0.028 A
(c)   I = 0.333 A
(d)   I = 0.500 A
(e)   I = ∞

QUESTION 21*

This and the next two questions pertain to the following situation.

An unpolarized electromagnetic wave is incident on a series of three linear polarizers, each with the polarization angle rotated at 45° with respect to the previous one.

If the initial intensity of the unpolarized light is I0, what is the intensity I1 transmitted through the first polarizer?

(a)   I1 = I0 / 4
(b)   I1 = I0 / 2
(c)   I1 = I0

QUESTION 22*

After the first polarizer, the light is linearly-polarized.  When it passes through the second polarizer:

(a)   only the electric field is reduced.
(b)   only the magnetic field is reduced.
(c)   both the electric and magnetic field are reduced.

QUESTION 23**

If the intensity of the polarized light after the first polarizer is I1, what is the intensity I3 as the light emerges from the stack?

(a)   I3 = 0
(b)   I3 = I1 / 2
(c)   I3 = I1 / 4
(d)   I3 = I1 / 8
(e)   I3 = I1 / 16

QUESTION 24**

Which one of the following is closest to the speed of light?

(a)   the speed of sound at an altitude of 36,000 feet
(b)   one billion feet per second
(c)   the orbital speed of the space shuttle
(d)   the circumference of the earth's orbit divided by 365 days
(e)   one trillion meters per second

QUESTION 25*

This and the next question pertain to the following situation.

A current of 5 A passes through a solenoid of length L = 30 cm and diameter 5 cm.  The number of turns of the solenoid is 250.

What is the value of the magnetic field inside the solenoid?

(a)   15.2 mT
(b)   5.2 mT
(c)   1 T
(d)   12.56 mT
(e)   0 T

QUESTION 26**

What is the value of the total energy stored in the solenoid?

(a)   4.57 J
(b)   10.7 J
(c)   6.42 mJ
(d)   200 J
(e)   2.176 mJ

QUESTION 27**

An electromagnetic wave transports equal amounts of energy in its electric and magnetic fields.

(T)   True
(F)   False

QUESTION 28*

Radio waves leaving the WILL-FM broadcast antenna have frequency 90.9 MHz. The wavelength of WILL's signal is:

(a)   3.3 m
(b)   102.7 m
(c)   2.7 × 1015 m

QUESTION 29**

Terrestrial astronomers detect a signal from a distant interstellar expedition's communication laser as a yellow-orange emission with wavelength 589 nm. The signal came from a starship at rest with respect to the earth. Later, the signal's wavelength is found to be 575 nm.

When it sent the 575 nm signal, the starship was moving

(a)   away from Earth.
(b)   towards Earth.

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.