### Spring 2009 Physics 212 Hour Exam 2(26 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 100. The exam period was 90 minutes; the mean was 76.0; the median was 78. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1**

Two capacitors are first charged, and then connected in the circuit shown. What happens to the charge on capacitor C1 after the switch is closed?

(a)   The charge on C1 decreases.
(b)   The charge on C1 stays the same.
(c)   The charge on C1 increases.

### QUESTION 2*

What would be the equivalent resistance between points A and B for the network of resistors shown? Assume that all resistors have the same value R.

(a)   (14/3) R
(b)   4 R
(c)   (7/5) R
(d)   (4/3) R
(e)   (2/5) R

### QUESTION 3*

This question and the next two refer to this circuit.

With the switch open as shown, what is the current I1?

(a)   I1 = -7/2 A
(b)   I1 = -1/2 A
(c)   I1 = 1/2 A
(d)   I1 = 3/2 A
(e)   I1 = 7/2 A

### QUESTION 4*

For this and the next question, the switch is closed.

What is the voltage across the 4 ohm resistor?

(a)   6 V
(b)   8 V
(c)   14 V
(d)   2 V
(e)   7 V

### QUESTION 5**

Which of the currents have changed in magnitude after the switch is closed?

(a)   Only I3 has changed in magnitude.
(b)   Only I2 and I3 have changed in magnitude.
(c)   I1, I2 and I3 have all changed in magnitude.

### QUESTION 6*

Three cylindrical resistors are connected in two different ways as shown. All resistors are made of the same material, and have areas and lengths as shown. Which one of the following accurately describes the relationship between the total resistance of configuration #1 (Rtot,1) and configuration #2 (Rtot,2)?

(a)   Rtot,1 > Rtot,2
(b)   Rtot,1 < Rtot,2
(c)   Rtot,1 = Rtot,2

### QUESTION 7*

This question and the next three pertain to this circuit.

At time t = 0 the switch is closed with the capacitor uncharged. The current through the capacitor right after the switch is closed is 0.0343 A.

What is the initial current through the 100 Ω resistor right after the switch is closed?

(a)   0.103 A
(b)   0.069 A
(c)   0.048 A

### QUESTION 8**

What is the final charge on the capacitor a long time after the switch is closed?

(a)   2.4 × 10-5 C
(b)   4.8 × 10-5 C
(c)   6.2 × 10-5 C
(d)   7.2 × 10-5 C
(e)   8.6 × 10-5 C

### QUESTION 9***

What is the time constant for charging the capacitor?

(a)   1.4 × 10-3 s
(b)   1.5 × 10-3 s
(c)   1.8 × 10-4 s

### QUESTION 10*

After a long time so that the capacitor is fully charged, the switch is opened. What is the time constant for discharging the capacitor?

(a)   1.4 × 10-3 s
(b)   1.5 × 10-3 s
(c)   1.8 × 10-3 s

### QUESTION 11*

A square one-turn loop (side a = 20 cm, resistance R = 5 Ω, mass m = 200 g) located in the xy plane coasts with initial velocity v0 = 10 m/s in the x-y plane parallel to the x-axis in a region of no magnetic field as shown in the diagram. At time t = 0 s the loop enters a region of constant uniform magnetic field B = 1.5 T directed in the -z direction (into the page). In the following questions neglect any effect of magnetic fields that might be created by an induced current in the loop.

What is the magnitude of the EMF induced in the loop just after it enters the field? (Remember 1 mV = 10-3V).

(a)   EMF = 150 mV
(b)   EMF = 750 mV
(c)   EMF = 3 V

### QUESTION 12*

What is the direction of the induced current in the loop just after the right (leading) edge of the loop enters the field?

(a)   clockwise
(b)   counterclockwise

### QUESTION 13**

What is the magnitude of the magnetic force on the loop just after the right (leading) edge of the loop enters the field?

(a)   F = 4 a B v R
(b)   F = a2 B v R
(c)   F = a2 B2 v R
(d)   F = a2 B2 v / R
(e)   F = a2 B2 v2 / R

### QUESTION 14**

This question and the next two pertain to this situation:

A tightly wound circular coil with radius a = 3 cm and N = 150 turns lies parallel to the x-y plane. The total resistance of the coil is 5 Ω. A spatially uniform magnetic field extends over the entire region of the coil and points in the +z direction (out of the page). The magnitude of the field varies with time as shown below (the maximum field B0 = 2 T is obtained at time t2 = 10 seconds). Neglect the effect of any B fields that might be created in the coil.

In what direction is the induced current flowing at time t1 = 5 seconds?

(a)   clockwise
(b)   counterclockwise

### QUESTION 15*

Compare I1, the magnitude of the current induced at time t1, to I3, the magnitude of the current induced at time t3 = 15 seconds.?

(a)   I1 < I3
(b)   I1 = I3
(c)   I1 > I3

### QUESTION 16**

What is I1, the magnitude of the current induced at time t1 = 5 seconds? (1 mA = 10-3 A)

(a)   I1 = 12 mA
(b)   I1 = 17 mA
(c)   I1 = 38 mA
(d)   I1 = 52 mA
(e)   I1 = 85 mA

### QUESTION 17*

This question and the next two refer to this figure:

A generator consisting of a single loop of wire with area A is used to light a bulb with resistance R. The coil is rotated with constant angular velocity ω.

At which angle θ (as defined in the figure) is the flux through the loop largest?

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

### QUESTION 18**

At which angle θ (as defined in the figure) is the voltage across the bulb largest?

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

### QUESTION 19**

At which angle θ (as defined in the figure) is the torque on the loop due to the magnetic field the largest?

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

### QUESTION 20*

This question and the next two refer to this situation:

An infinitely long wire carries a current Iw = 3.0 A (out of the page), and lies along the axis of symmetry of a cylindrical shell of inner radius a = 2.70 cm and outer radius b = 7.60 cm. The shell carries a current I2 = 1.8 A (into the page) distributed with uniform current density J.

Find the magnetic field strength at a distance r = 2.00 cm from the wire.

(a)   B = 0
(b)   B = 1.2 × 10-5 T
(c)   B = 1.8 × 10-5 T
(d)   B = 3.0 × 10-5 T
(e)   B = 4.8 × 10+5 T

### QUESTION 21**

Find the magnetic field strength at a distance r = 5.40 cm from the wire (inside the shell):

(a)   B = 2.9 × 10-6 T
(b)   B = 6.7 × 10-6 T
(c)   B = 8.2 × 10-6 T

### QUESTION 22*

Find the magnetic field strength at a distance r = 9.00 cm from the wire (outside the shell).

(a)   B = 2.7 × 10-6 T
(b)   B = 4.0 × 10-6 T
(c)   B = 0

### QUESTION 23*

This question and the next two refer to this situation:

An infinitely long wire carries a current I1 = 23 A. Another wire in the shape of a rectangular loop with sides a = 0.09 m and b = 0.20 m carries a current I2 = 15 A, and is placed near the infinitely long wire as shown in the figure below. (The side of the loop closest to the wire is a distance x = 0.01 m away from it.)

Calculate the z component of the magnetic field at the center of the rectangular loop (point P) due to the infinitely long wire.

(a)
(b)
(c)

### QUESTION 24**

Find the x component of the force on the side BC of the wire, due to the infinitely long wire.

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

### QUESTION 25**

What is the direction of the net force on the loop?

(a)   -x
(b)   +x
(c)   There is no direction since F = 0.

### QUESTION 26*

A positively charged particle is injected into a region occupied by a uniform B field pointing out of the paper. The particle's initial velocity, v0, is straight upward. It emerges from the B field region at position X, after travelling for a time Δt through the field. If the particle was injected instead with velocity 2v0, it would

(a)   emerge at the same position X, but after a different amount of time Δt.

(b)   emerge at a different position X, but after the same amount of time Δt.

(c)   emerge at a different position X and after a different amount of time Δt.

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.