### Fall 2008 Physics 212 Hour Exam 2(27 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 117. The exam period was 90 minutes; the mean was 94.1; the median was 98. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the next four questions refer to the situation described here.

The figure depicts a square wire coil with 4 loops. The length of each side of the square is L. The coil is situated in a region of constant magnetic field B = 0.2 T pointing in the +y direction. A current I = 20 amps flows in the coil in the direction shown (the black arrowhead indicates the current direction on the side of the square nearest you.) The square coil makes an angle of α with the xz-plane and the coil has a magnetic dipole moment with magnitude 25 A m2.

What is the length of a side of the square loop?

(a)   L = 0.44 m
(b)   L = 0.56 m
(c)   L = 0.62 m

### QUESTION 2*

What is the magnitude of the torque on the loop with α = 30°?

(a)   2.5 N m
(b)   3.3 N m
(c)   4.1 N m
(d)   4.6 N m
(e)   5.0 N m

### QUESTION 3*

What is the direction of the torque on the loop when α = 30°?

(a)   clockwise (decreasing α)
(b)   counterclockwise (increasing α)

### QUESTION 4**

At which angle α does the coil have the lowest potential energy?

(a)   α = 0°
(b)   α = 45°
(c)   α = 90°

### QUESTION 5*

What is the magnitude of the change in potential energy of the coil when it is rotated from α = 30° to α = 0° ?

(a)   | ΔU |  =  0.67 J
(b)   | ΔU |  =  1.00 J
(c)   | ΔU |  =  1.25 J
(d)   | ΔU |  =  2.00 J
(e)   | ΔU |  =  2.50 J

### QUESTION 6**

This and the next two questions refer to the situation described here.

Two fixed conductors are connected by a resistor R = 20 Ω. The two fixed conductors are separated by L = 2.5 m and lie horizontally. A moving conductor of mass m slides on them at a constant speed v, producing a current of 3.75 amps. A magnetic field (shown by the black dots in the figure) with magnitude 5 T points out of the page.

In which direction does the current flow through the moving conductor when the bar is sliding in the direction shown?

(a)   to the right
(b)   to the left

### QUESTION 7**

At what speed is the bar moving?

(a)   v = 1 m/s
(b)   v = 3 m/s
(c)   v = 5 m/s
(d)   v = 6 m/s
(e)   v = 9 m/s

### QUESTION 8*

What is the force on the bar?

(a)   F = 28 N
(b)   F = 37 N
(c)   F = 47 N

### QUESTION 9**

This and the next three questions refer to the situation described here.

The values of all circuit elements are given in the figure. The capacitor is initially uncharged. Then, at time t = 0, the switch is closed.

What is the current through the battery immediately after the switch is closed?

(a)   I = 0.6 A
(b)   I = 0.9 A
(c)   I = 1.2 A

### QUESTION 10*

After the switch is closed, the current through resistor R1

(a)   increases with time.
(b)   decreases with time.
(c)   remains constant with time.

### QUESTION 11**

Find the charge on the capacitor a long time after the switch is closed.

(a)   Q = 2.0 μC
(b)   Q = 3.0 μC
(c)   Q = 4.0 μC
(d)   Q = 5.0 μC
(e)   Q = 6.0 μC

### QUESTION 12**

A long time after the switch has been closed, it is re-opened. What is the time constant for discharging the capacitor?

(a)   2.4 μs
(b)   3.3 μs
(c)   6.7 μs
(d)   10.0 μs
(e)   30.0 μs

### QUESTION 13*

This and the next three questions all concern the circuit shown below.

With the switch open, what is the current I1? (A positive sign means that current flows in the direction of the arrow.):

(a)   -0.20 A
(b)   -0.05 A
(c)   +0.05 A
(d)   +0.20 A
(e)   +0.35 A

### QUESTION 14*

Once the switch is closed, what is the power dissipated in the 50 Ω resistor?

(a)   0.13 W
(b)   1.39 W
(c)   2.47 W

### QUESTION 15*

How much current passes through the closed switch?

(a)   0.05 A
(b)   0.09 A
(c)   0.12 A
(d)   0.33 A
(e)   0.47 A

### QUESTION 16**

With the switch closed, what is the voltage difference, VA - VB?

(a)   VA - VB  =  10 - 10 I1 - 5 I2
(b)   VA - VB  =  10 + 10 I1 + 5 I2
(c)   VA - VB  =  -6 + 50 I1 + 15 I2
(d)   VA - VB  =  6 + 50 I1 - 15 I2
(e)   VA - VB  =  6 - 50 I1 + 15 I2

### QUESTION 17**

A rectangular wire loop travels to the right with a constant velocity, starting in a region of no magnetic field, moving into a region with a constant magnetic field pointing into the page (shaded rectangle below), and continuing into a region of no magnetic field.

Which one of the plots at right best represents the induced current in the loop (Iloop) as a function of its position as it travels from the left through these three regions. Note: A positive Iloop means that current flows counter-clockwise.

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

### QUESTION 18*

This and the next question refer to the situation described here.

Consider the two cases shown below. In each case a conductor carries the same total current I = 2 amps into the page, and in each case the current is uniformly distributed over the cross-section of the conductor.

In Case 1 the conductor is a cylindrical shell of outer radius R0 = 10 cm and inner radius R1 = 7.5 cm. In Case 2 the conductor is a solid cylinder having the same outer radius R0 = 10 cm.

Compare B1(a), the magnitude of the magnetic field at point a (r = 5 cm) in Case 1, to B2(a), the magnitude of the magnetic field at point a (r = 5 cm) in Case 2.

(a)   B1(a) < B2(a)
(b)   B1(a) = B2(a)
(c)   B1(a) > B2(a)

### QUESTION 19*

What is the y component of the magnetic field at point b (r = 15 cm) in Case 2 ?

(a)   -2.67 × 10-6 T
(b)   -1.33 × 10-6 T
(c)   0 T
(d)   1.33 × 10-6 T
(e)   2.67 × 10-6 T

### QUESTION 20**

Two long conductors, oriented perpendicular to the page and parallel to each other, carry current of the same magnitude. The current in the left conductor runs into the page and the current in the right conductor runs out of the page.

Which one of the statements at right best describes the integral of B.dL along just the left most segment of the path (i.e. b → c)?

(a)
(b)
(c)

### QUESTION 21*

This and the next question refer to the situation described here.

An infinite solid cylindrical conductor of radius a = 3 cm centered on the z-axis carries a current I1 = 1 A. The current is uniformly distributed over its cross section and is directed out of the page (positive z-direction). A coaxial infinite, thin cylindrical conducting shell of radius b = 8 cm carries a current I2 = 4 A, into the page (negative-z direction).

What is the magnitude of the B field inside the inner cylinder at a radius of 2.0 cm from the central axis?

(a)   0
(b)   1.79 × 10-6 T
(c)   2.77 × 10-6 T
(d)   3.58 × 10-6 T
(e)   4.44 × 10-6 T

### QUESTION 22*

Which one of the following plots best represents the y-component of the magnetic field By at points along the positive x-axis [ i.e. at all points (x,y) = (x,0) ] ?

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

### QUESTION 23*

A strong magnet is brought near to a diamagnetic material, such as a grape.

(a)   The diamagnetic material is repelled by the magnet.
(b)   The diamagnetic material is not attracted or repelled by the magnet. Nothing happens.
(c)   The diamagnetic material is attracted to the magnet.

### QUESTION 24**

A strong magnet is brought near to a paramagnetic material, such as aluminum.

(a)   The paramagnetic material is repelled by the magnet.
(b)   The paramagnetic material is not attracted or repelled by the magnet. Nothing happens.
(c)   The paramagnetic material is attracted to the magnet.

### QUESTION 25**

This and the next question refer to the situation described here.

A negatively charged particle (q < 0) enters a region with uniform magnetic field B = Boz. (The region with the field is shaded.) The particle has initial velocity v = voy along the y axis as shown at right.

The particle bends around in a semicircle and exits the field region a distance L from the origin. Does it exit at x = -L or at x = +L ?

(a)   x = +L
(b)   x = -L

### QUESTION 26*

What is the mass of the particle?

(a)   2 vo / |q| Bo L
(b)   Bo L / 2 |q| vo
(c)   |q| L / Bo vo
(d)   |q| Bo L / 2 vo
(e)   |q| Bo / 2 L vo

### QUESTION 27*

Two infinitely long, parallel wires carry steady currents I1 and I2 and are separated by a transverse distance d. If the currents in each wire are flowing in the same direction:

(a)   each wire experiences an attractive force, directed towards the other wire.
(b)   each wire experiences no net force.
(c)   each wire experiences a repulsive force, directed away from the other wire.

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.