### Spring 2010 Physics 212 Hour Exam 2(25 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 96. The exam period was 90 minutes; the mean was 72.1; the median was 74. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This question and the next one pertain to the following situation:

Four infinite wires carry currents parallel to the z-axis as shown in the figure. Each wire is spaced from the z-axis by a meters. The magnitude of the current in each of the wires is equal to I0. Two of the wires carry current in the positive z-direction and two of the wires carry current in the negative z-direction.

What is the magnetic field B(0) at the origin?

(Hint: Use the principle of superposition and the right hand rule to solve this. Keep track of the contribution from each wire.)

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

### QUESTION 2*

If the current flowing in negative z direction is reversed so that now all the wires carry equal current in the positive z-direction, which one of the following statements is true?

(a)   The magnetic field everywhere stays the same.
(b)   The magnetic field everywhere is one half what it was before.
(c)   The magnetic field at the origin goes to zero.

### QUESTION 3*

This question and the next one pertain to the following situation:

An infinite coaxial cable consists of a solid center conductor of radius 0.01 meter, and an outer conducting cylindrical shell of radius 0.1 meter. A small section of the cable is shown in the figure. A current of 4 amperes flows to the right uniformly distributed in the center conductor and a current of 2 amperes flows to the left uniformly distributed on the outer conductor. The center of the coaxial cable is the axis of cylindrical symmetry.

What is the magnitude of the magnetic field 0.8 meter from the axis of cylindrical symmetry?

(a)   2.0 × 10-7 tesla
(b)   5.0 × 10-7 tesla
(c)   8.0 × 10-7 tesla
(d)   1.0 × 10-6 tesla
(e)   1.5 × 10-6 tesla

### QUESTION 4*

Now let the total current that flows to the left on the outer conducting cylinder be varied. The magnitude of the magnetic field in between the center conductor and the outer conductor is dependent on the current that is carried by the outer conductor.

(T)   True
(F)   False

### QUESTION 5*

This question and the next one pertain to the following situation:

Between time t = 0 and t = τ the magnetic field in the region of space pertaining to this problem is given by B(t) = B0(1-t/τ)z, where B0 is a positive number. At earlier times the field is constant and is given by B(t) = B0z and at later times the field is zero. This means that the magnetic field at time t = 0 points in the positive z-direction and has a magnitude of B0 and then it linearly decreases in magnitude reaching zero at time t = τ. This is shown on the graph below. A conducting loop of area A that incorporates a resistor with a resistance R0 lies in the x-y plane as shown in the adjacent figure.

Which one of these statements regarding the current in the loop during the time interval between t = 0 and t = τ is true?

(a)   Since there is no battery, there is no current.
(b)   There is a current that flows counter-clockwise as viewed from above.
(c)   There is a current that flows clockwise as viewed from above.

### QUESTION 6*

When 0 < t < τ, the magnitude of the EMF integrated around the loop equals:

(a)   ε = 2τR0 / B0
(b)   ε = AB0 / τ
(c)   ε = AτB0
(d)   ε = τB0 / R0
(e)   ε = AR0B0 / 2τ

### QUESTION 7**

This question and the next one pertain to the following situation:

Two batteries are arranged in a circuit with two resistors as shown in the figure. The resistance of each resistor is not given, but the indicated currents are observed to flow through the two resistors. (Hint: Redraw the circuit to see explicitly what circuit elements are in series and which are in parallel. Pay attention to the polarity of the batteries in the figure.)

Which battery supplies the most power to the resistors?

(a)   the 20 V battery
(b)   the 30 V battery

### QUESTION 8*

Find the resistance R2.

(a)   12.5 Ω
(b)   10 Ω
(c)   5 Ω
(d)   4 Ω
(e)   2 Ω

### QUESTION 9**

This question and the next two pertain to the following situation:

A circuit consists of a capacitor, two 10 Ω resistors, and a 100 V battery connected as shown in the figure. The switch is closed (connected) at time t = 0. Assume that the capacitor is uncharged before the switch is closed.

It is observed that the charge stored on the capacitor as a function of time while it charging is given by

Find the capacitance C of the capacitor

### QUESTION 10*

The power delivered by the battery is largest at t = 0.

(T)   True
(F)   False

### QUESTION 11*

Which one of these statements is true concerning the current flowing through the two resistors?

(a)   At t = 0 the same current flows through the two resistors.
(b)   At t = the same current flows through the two resistors.
(c)   At t = 0 twice the current flows through one resistor compared to the other.

### QUESTION 12*

This question and the next three pertain to the following situation:

A circuit is constructed out of a 0.01 F capacitor, four resistors, and a 30 V battery connected as shown in the figure. The switch is closed (connected) at time t = 0. Assume that the capacitor is uncharged before the switch is connected.

At t = 0 the current flowing though the battery is:

(a)   2.06 A
(b)   1.08 A
(c)   2.54 A

### QUESTION 13**

At t = the right plate of the capacitor is positively charged.

(T)   True
(F)   False

### QUESTION 14**

Find the energy stored in the capacitor at t = .

(a)   1.125 J
(b)   1.000 J
(c)   0.750 J
(d)   0.125 J
(e)   0.050 J

### QUESTION 15**

If we replace the two 15 Ω resistors with two 20 Ω resistors what would happen to the energy stored in the capacitor at

(a)   The stored energy in the capacitor with 20 Ω resistors is larger than the stored energy with 15 Ω resistors.
(b)   The stored energy in the capacitor with 20 Ω resistors is smaller than the stored energy with 15 Ω resistors.
(c)   The stored energy in the capacitor with 20 Ω resistors is equal to the stored energy with 15 Ω resistors.

### QUESTION 16*

This question and the next one pertain to the following situation:

A neutral, conducting rod of length L = 0.4 m is moving with constant speed v = 2 m/s in the positive x direction in the presence of a magnetic field B = 0.35 T directed into the page as shown.

The bottom end of the rod has

(a)   excess + charge.
(b)   excess - charge.

### QUESTION 17**

What is the magnitude of the electric field between the ends of the rod?

(a)   0.7 V/m
(b)   0.28 V/m
(c)   1.75 V/m

### QUESTION 18*

This question and the next three pertain to the following situation:

A single circular loop of wire of radius R = 0.24 m carries current I = 0.4 A, and is oriented as shown in the diagram. A constant magnetic field points along the negative y-direction having magnitude B = 0.7 T. To begin with, the loop is fixed in space.

In the diagram at the right, the two arrows labeled "a)" and "b)" denote two possible directions for the magnetic moment of the loop. Which is actually the correct direction?

(a)   Orientation "a)" is correct for the magnetic moment.
(b)   Orientation "b)" is correct for the magnetic moment.

### QUESTION 19*

What is the magnitude of the torque, τ, acting on the loop?

(a)   0.025 N⋅m
(b)   0.044 N⋅m
(c)   0.066 N⋅m
(d)   0.21 N⋅m
(e)   0.37 N⋅m

### QUESTION 20*

Now the loop is released. A short time later, it has rotated a little bit. Which of the following figures shows the orientation of the loop a short time later? (The dashed line shows the original position of the loop.)

(a)
(b)

### QUESTION 21**

For this problem assume that the loop starts in the original position and then an external agent rotates it counterclockwise by 60° until it is vertical, as shown in the diagram at the right. For this rotation the potential energy of the system

(a)   increases.
(b)   decreases.

### QUESTION 22*

This question and the next one pertain to the following situation:

Two charged particles enter a region of constant and uniform magnetic field directed out of the page (positive z direction) through a small opening traveling along the positive y-axis. The path taken by the two particles is shown in the diagram. Both particles enter the region of magnetic field with the same speed and both have the same magnitude charge.

What type of charge are the two particles?

(a)   Particle #1 is + and particle #2 is -.
(b)   Particle #1 is - and particle #2 is +.

### QUESTION 23**

Now consider only particle #1. What is the distance d1 as shown in the diagram? Assume for this problem that B = 1.58 T, v = 500 m/s, m1 = 2 × 10-9 kg and the magnitude of charge q1 is 3.4 × 10-6 C.

(a)   0.186 m
(b)   0.215 m
(c)   0.372 m
(d)   0.487 m
(e)   0.669 m

### QUESTION 24***

An electron (q = -1.6 × 10-19 C) enters a region of magnetic field B = 0.2 T directed into the page traveling horizontally at speed v = 3 × 104 m/s, as shown. What is the direction, and magnitude, of the electric field E needed so that the electron travels in a straight line? (Neglect gravity.)

(a)   9.6 × 10-16 V/m directed toward the bottom of the page
(b)   6.0 × 103 V/m directed toward the bottom of the page
(c)   9.6 × 10-16 V/m directed toward the top of the page
(d)   6.0 × 103 V/m directed toward the top of the page
(e)   9.6 × 10-16 V/m directed out of the page.

### QUESTION 25**

Consider the 3 situations depicted below, all involving a conducting rod of length L moving in the presence of a magnetic field. In which situation(s) is there an induced voltage between opposite ends of the rod?

(a)   Situation 1
(b)   Situation 2
(c)   Situation 3
(d)   Situations 2 and 3
(e)   Situations 1, 2 and 3

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.