### Fall 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 120. The exam period was 90 minutes; the mean was 92.0; the median was 96. 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:

This circuit has three batteries with voltages V1, V2 and V2, three standard resistors of resistance R1 and a light bulb with resistance R2.

Which one of the choices listed on the right is an expression for the magnitude of the current I in terms of V1, V2, R1 and R2?

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

### QUESTION 2**

The potential at point A is ____________ the potential at point B.

(a)   lower than
(b)   the same as
(c)   higher than

### QUESTION 3*

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

Three resistors, three capacitors, a battery and two switches are connected in the circuit shown below. The values of all circuit elements are given in the figure. Originally, the switches S1 and S2 are open (as shown) and all of the capacitors are uncharged. At time t = 0, both switches are closed.

What is the current I1 through resistor R1 immediately after the switches are closed?

(a)   I1 = 0 A
(b)   I1 = 1.8 A
(c)   I1 = 2.5 A
(d)   I1 = 3.8 A
(e)   I1 = 4.7 A

### QUESTION 4*

A very long time after the switches are closed, the current I2 is:

(a)   I2 > 0
(b)   I2 = 0
(c)   I2 < 0 (i.e. opposite the direction shown)

### QUESTION 5*

What is the charge Q2 on capacitor C2 a very long time after the switches are closed?

(a)   Q2 = 0 μC
(b)   Q2 = 33 μC
(c)   Q2 = 90 μC
(d)   Q2 = 180 μC
(e)   Q2 = 270 μC

### QUESTION 6**

After a very long time with both switches in the closed position, switch S2 is reopened. How long (t1/e) does it take for the charge on capacitor C2 to drop to 1/e (36.8%) of its fully-charged value (i.e. of the value it had just before S2 was reopened)?

(a)   t1/e = 1200 μsec
(b)   t1/e = 1500 μsec
(c)   t1/e = 3000 μsec
(d)   t1/e = 3600 μsec
(e)   t1/e = 4800 μsec

### QUESTION 7*

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

An electron of mass m and charge q is accelerated to the right (in the plane of the page) from rest through a potential difference V. The electron then enters a region, defined by x > 0, containing a uniform magnetic field.

When the electron enters the region with the magnetic field the force on it is directed

(a)   toward the top of the page.
(b)   toward the bottom of the page.
(c)   into the page.

### QUESTION 8*

When the electron is in the magnetic field region, its speed v.

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

### QUESTION 9**

How much time T does the electron spend in the magnetic field region?

(a)   T = 1.2 × 10-15 s
(b)   T = 7.5 × 10-12 s
(c)   T = 6.0 × 10-11 s
(d)   T = 8.3 × 10-8 s
(e)   T = 4.1 × 10-5 s

### QUESTION 10**

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

A rectangular wire loop of height h and width w, centered on the origin, carries current I in the direction shown in the figure. The angle between the positive x-axis and the plane of the loop is θ, defined as shown in the figure below. (When θ = 0 the loop lies in the x-z plane.) This entire region of space is filled with a uniform external magnetic field B pointing in the +x direction.

When θ = 60°, the force on the leg of length h with the upward-going current is in the

(a)   positive x direction.
(b)   negative x direction.
(c)   positive y direction.
(d)   negative y direction.
(e)   positive z direction

### QUESTION 11*

The magnitude of the work, |W|, involved in the rotation of the loop from θ = 0° to θ = 60° is:

(a)   |W| = 9.09 × 10-5 J
(b)   |W| = 2.37 × 10-4 J
(c)   |W| = 4.25 × 10-4 J
(d)   |W| = 5.87 × 10-4 J
(e)   |W| = 8.13 × 10-4 J

### QUESTION 12**

When the loop rotates from θ = 0° to θ = 60°, the external magnetic field

(a)   does no work on the loop.
(b)   does positive work on the loop.
(c)   does negative work on the loop.

### QUESTION 13**

Two long wires carry currents I1 and I2 as shown in the figure. The first wire runs parallel to the x axis but is a distance d above the x-y plane. The second wire lies along the y axis and passes through the origin.

What is the direction of the torque on the wire carrying I1 due to the current I2 in the other wire?

(a)   in the positive y direction
(b)   in the positive z direction
(c)   in the negative y direction

### QUESTION 14*

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

A solid, infinitely-long, conducting rod has radius a = 15 cm and lies along the z axis. It carries a current I = 30 A in the +z direction. The current is uniformly distributed across the rod.  It is surrounded, at a distance b = 30 cm, by a thin coaxial conducting shell that carries a current of the same magnitude, but directed in the -z direction.

Find the magnitude B of the magnetic field at a distance of 10 cm from the origin.

(a)   B = 2.67 × 10-5 T
(b)   B = 3.52 × 10-5 T
(c)   B = 4.80 × 10-5 T
(d)   B = 6.15 × 10-5 T
(e)   B = 7.20 × 10-5 T

### QUESTION 15*

The direction of the magnetic field at the point (x = 0, y = 10 cm) is in the

(a)   negative x direction
(b)   negative y direction
(c)   positive y direction

### QUESTION 16*

Which of the following drawings most accurately represents the component By of the magnetic field at points on the positive x-axis?

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

### QUESTION 17*

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

A rectangular wire loop of height h, width w and net electrical resistance R lies in the x-y plane. As shown in the figure below, there is a region of space at -1.5w < x < 0 in which there is a magnetic field pointing in the -z direction. In order to determine the magnitude of this field, a student pulls the wire loop through the magnetic field region at a constant velocity v in the +x-direction, and measures the current I induced in the loop during this process.

If, when the leading edge, A, of the loop is located at xA = -w, the student measures a current of 20 × 10-6 amps, what is the magnitude B of the magnetic field?

(a)   B = 0.12 T
(b)   B = 0.31 T
(c)   B = 0.57 T
(d)   B = 0.99 T
(e)   B = 1.15 T

### QUESTION 18**

When the leading edge, A, of the loop is located at xA = +w/2, what is the direction of the current flowing in the loop?

(a)   clockwise
(b)   counter-clockwise
(c)   No current flows in the loop in this situation.

### QUESTION 19**

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

The figure at right shows a circular wire loop of total resistance R. The loop is contained within a region having a uniform magnetic field B pointing out of the page, and is attached to a motor that keeps it rotating around the y-axis in a clockwise direction (when looking in the negative y-direction) at constant angular velocity ω. The loop is initially parallel to the x-y plane (the plane of the paper), as shown.

Which one of the following graphs best represents the EMF induced in the loop as a function of time? (ε changes sign if the induced current changes direction; ε = 0 is denoted on the graphs. In the initial (t = 0) position shown in the figure above, ε is defined to be positive if it leads to clockwise current in the loop).

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

### QUESTION 20**

When the loop has rotated to the y-z plane, what is the magnitude |ε| of the induced EMF?

(a)   |ε| = 0 V
(b)   |ε| = 0.0563 V
(c)   |ε| = 0.125 V
(d)   |ε| = 0.224 V
(e)   |ε| = 0.418 V

### QUESTION 21**

If the resistance R of the loop is increased (but all other parameters remain unchanged) the maximum torque supplied to rotate the loop

(a)   increases.
(b)   remains the same.
(c)   decreases.

### QUESTION 22*

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

Three identical resistors are connected to a battery, an inductor, and a switch as shown in the figure. (The values of all circuit elements are given below the figure.) The switch has been open for a very long time, and then it is closed at time t = 0.

Calculate the current delivered by the battery immediately after the switch is closed.

(a)   0.353 A
(b)   0.706 A
(c)   0.998 A
(d)   1.22 A
(e)   1.38 A

### QUESTION 23**

Immediately after the switch is closed, the voltage VL across the inductor is

(a)   VL = 0 V
(b)   VL = 6 V
(c)   Neither of the above answers is correct.

### QUESTION 24*

After the switch has been closed for a very long time, how much energy EL is stored in the inductor?

(a)   EL = 3.30 × 10-6 J
(b)   EL = 5.62 × 10-6 J
(c)   EL = 8.63 × 10-6 J
(d)   EL = 1.07 × 10-5 J
(e)   EL = 1.12 × 10-5 J

### QUESTION 25*

After the switch has been closed for a very long time, a steady current has been established through the inductor. The switch is then reopened. What fraction of this current, fI, remains after a time interval of Δt = 3 μsec has elapsed?

(a)   fI = 0.0521
(b)   fI = 0.0926
(c)   fI = 0.158
(d)   fI = 0.201
(e)   fI = 0.236

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.