### Fall 2003 Physics 102 Hour Exam 2(28 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 ***.

This exam consists of 28 questions; 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 118. When the exam was given, the mean was 91.0; the median was 93. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

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

A long straight wire carries a current of 30 A as shown in the figure. A proton (q = 1.6 × 10-19 C) is moving with velocity 2 × 108 m/s. The velocity makes an angle of 20° with the direction of the wire. At the instant considered in this problem, the proton is 0.25 m away from the wire.

What is the magnitude of the magnetic field due to the wire at the position of the proton?

(a)   1.9 × 10-7 T
(b)   8.2 × 10-6 T
(c)   5.3 × 10-6 T
(d)   2.4 × 10-5 T
(e)   2.6 × 10-4 T

### QUESTION 2*

What is the magnitude of the magnetic force on the proton?

(a)   7.7 × 10-16 N
(b)   9.5 × 10-16 N
(c)   3.7 × 10-15 N
(d)   4.9 × 10-15 N
(e)   6.2 × 10-14 N

### QUESTION 3**

Which one of the following is correct for the direction of the magnetic force on the proton?

(a)   The force is in the plane of the paper.
(b)   The force is perpendicular to the plane of the paper.

### QUESTION 4*

This and the next question pertain to the following situation.

A plastic cube measuring 1 m on each side is placed in a uniform magnetic field of magnitude 1 T which points in the vertical direction, as in the diagram below.

A charged particle enters the cube at point a and exits at point b, leaving a track (dashed line) which is a quarter of a circle. Note that the plastic cube does not interfere with the motion of the charged particle and has permeability μ0 (treat the cube as vacuum for the purposes of this problem). The magnitude of the charge is 1.6 × 10-19 C and its velocity is 4.8 × 107 m/s.

What is the mass of the charged particle?

(a)   2.49 × 10-28 kg
(b)   1.62 × 10-25 kg
(c)   1.67 × 10-27 kg
(d)   9.08 × 10-31 kg
(e)   1.88 × 10-28 kg

### QUESTION 5*

What is the sign of the charge?

(a)   positive
(b)   negative

### QUESTION 6**

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

Two identical solenoids are arranged as shown in the figure above. The current in each solenoid is the same. The two solenoids are now joined to make one solenoid, as shown in the figure below. The current in this solenoid is the same as the current in each of the original solenoids.

The magnetic field in this solenoid, compared with the magnetic field in each of the original solenoids, is

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

### QUESTION 7*

If the current in this solenoid is reversed such that it flows in the opposite direction, the magnetic field in the solenoid will

(a)   reverse direction.
(b)   stay the same.

### QUESTION 8**

The self inductance of this solenoid, in comparison with the self inductance of one of the two original solenoids, is

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

### QUESTION 9*

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

A rectangular loop of wire has sides with lengths 1.5 m and 2.0 m as shown in the figure below. The loop has one turn of wire and carries a current of 13 A in the direction shown on the cd side. In the same plane as the loop is a uniform magnetic field of magnitude 4.6 mT. The field makes an angle of 37° with the bd (and ac) sides of the loop, as in the figure.

What is the magnitude of the magnetic force on the cd side of the loop?

(a)   4.3 × 10-3 N
(b)   6.7 × 10-2 N
(c)   9.6 × 10-2 N
(d)   1.3 × 10-1 N
(e)   2.6 × 10-1 N

### QUESTION 10*

The direction of the force on the cd side of the loop is

(a)   out of the page.
(b)   into the page.

### QUESTION 11**

The direction of the force on the ac side of the loop is

(a)   out of the page.
(b)   into the page.

### QUESTION 12*

The magnitude of the torque on the loop is

(a)   7.2 × 10-3 Nm
(b)   1.1 × 10-2 Nm
(c)   2.9 × 10-2 Nm
(d)   4.6 × 10-2 Nm
(e)   1.8 × 10-1 Nm

### QUESTION 13**

The torque will tend to rotate the loop around a certain axis. Which of the axes labeled (1), (2), or (3) is the correct axis of rotation?

(a)   (1)
(b)   (2)
(c)   (3)

### QUESTION 14*

This and the following question pertain to the following situation.

A constant magnetic field is pointing into the page within the region indicated by "x" marks in the figure below.

Three identical rectangular loops of conducting wire are lying flat on the page and are moving to the right with the same constant velocity. The resistance is the same for each loop.

Which one of the following statements is true about the induced emf ε in the loops?

(a)   εB > εA > εC
(b)   εA > εC > εB
(c)   εC > εA > εB

### QUESTION 15**

At the instant shown, the current induced in loop C

(a)   flows clockwise.

(b)   flows counterclockwise.

(c)   is zero.

### QUESTION 16**

Two conductors are sliding toward each other on conducting rails. The velocity of each conductor is shown on the figure. There is a magnetic field of 2.2 mT pointing out of the page.

What is the magnitude of the emf in the circuit composed of the two moving conductors and the part of the rails between the two conductors?

(a)   20.9 mV
(b)   13.2 mV
(c)   7.7 mV
(d)   5.5 mV
(e)   0.0 mV

### QUESTION 17***

A laser beam (which is an electromagnetic wave) is focused on an atom with cross-sectional area 10-12 m2. The atom absorbs 1 mW average power from the laser beam.

What is the peak electric field of the laser beam at the atom?

(a)   1230 V/m
(b)   1.23 × 109 V/m
(c)   1.32 V/m
(d)   7.42 × 105 V/m
(e)   8.68 × 105 V/m

### QUESTION 18*

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

Two polarizers are arranged as in the diagram above. In between the polarizers is a perfectly transparent crystal that rotates the polarization of light that passes through it by 45° in the direction indicated on the diagram by the large filled arrow. Unpolarized light with intensity I0 is sent from point A in the positive z direction (toward point C).

What is the intensity at point B?

(a)   0
(b)   I0 / 3
(c)   I0 / 2

### QUESTION 19**

What is the intensity at point C?

(a)   0
(b)   I0 / 2
(c)   I0 / √2

### QUESTION 20*

Now light polarized along the x direction is sent from point C in the negative z direction (toward point A). What is the intensity at point A?

(a)   0
(b)   I0
(c)   I0 / √2

### QUESTION 21***

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

An antenna is connected to a tunable capacitor with capacitance C and a resistor in order to make the circuit in the diagram. The fixed capacitor, inductor, and resistor have values 0.03 μF, 1 μH, and 50 Ω.

What capacitance C should an engineer tune the capacitor to in order to make the circuit resonant with a broadcast at 580 kHz (local station WILL)?

(a)   4.5 × 10-8 F
(b)   1.5 × 10-9 F
(c)   7.3 × 10-8 F
(d)   1.7 × 10-8 F
(e)   1.2 × 10-8 F

### QUESTION 22*

Now that the capacitor is tuned to receive station WILL, the engineer looks for a signal. What is the impedence of the circuit for a signal at 580 kHz?

(a)   25 Ω
(b)   50 Ω
(c)   100 Ω
(d)   10 Ω
(e)   12 Ω

### QUESTION 23*

What is the wavelength of the 580 kHz electromagnetic wave broadcast by WILL?

(a)   1.10 m
(b)   517 m
(c)   0.350 m
(d)   605 m
(e)   1050 m

### QUESTION 24**

Once the engineer tunes the circuit to pick up WILL, which one of these phasor diagrams best represents the circuit?

(a)
(b)
(c)

### QUESTION 25*

This and the next question pertain to the following situation.

A mechanical crank is used to turn a rectangular loop with area 0.5 m2 at angular frequency Ω in the presence of a magnetic field B = 2 T as shown above. The 30 V peak EMF produced in the loop results in a peak voltage across the primary of the transformer of Vp = 30 V. The secondary windings are connected to a 10 Ω resistor. The secondary coil has three times as many windings as the primary coil.

What is the peak voltage across the secondary of the transformer?

(a)   Vs = 30 V
(b)   Vs = 90 V
(c)   Vs = 10 V

### QUESTION 26*

What is the average power dissipated in the 10 Ω resistor?

(a)   565 W
(b)   103 W
(c)   405 W
(d)   210 W
(e)   698 W

### QUESTION 27*

This and the next question pertain to the following situation.

A series RLC circuit is connected to a generator that operates at a frequency of 1 Hz. This circuit is used to run a pacemaker, which is connected in parallel to the inductor (the pacemaker has a very high resistance and does not change the operation of the circuit). The resistor, capacitor, and inductor have values R = 10 Ω, C = 1 mF, and L = 20 H.

What is the rms current in the circuit when the rms voltage across the inductor is 1 kV?

(a)   7.96 A
(b)   1.23 A
(c)   10.3 A
(d)   1.05 A
(e)   6.54 A

### QUESTION 28*

What should the rms voltage of the generator be so that the rms voltage across the inductor (and the pacemaker) is 1 kV?

(a)   305 V
(b)   278 V
(c)   126 V
(d)   558 V
(e)   1.00 V

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.