### Fall 2009 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 118. The exam period was 90 minutes; the mean was 90.2; the median was 93. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This question and the next two pertain to the circuit shown here.

What is the voltage, V3, across R3?

(a)   1.64 volts
(b)   2.64 volts
(c)   3.64 volts
(d)   4.36 volts
(e)   5.36 volts

### QUESTION 2*

If R2 is increased to 10 Ω, then the voltage, V3, across resistor R3

(a)   increases.
(b)   decreases.

### QUESTION 3*

Positive values for currents I1, I2, I3 and I4 indicate current flow in the direction shown in the figure. Which one of the following equations is not correct?

(a)   I1R1 + I3R3 - V = 0
(b)   V - I1R1 - I2R2 - I4R4 = 0
(c)   I2R2 - I4R4 - I3R3 = 0
(d)   I1 = I2 + I3
(e)   I1R1 + I2R2 + I4R4 - V = 0

### QUESTION 4**

In the circuit from the preceding three questions, a wire is added as shown in the figure below. The voltage, V, and resistors R1 through R4 are the same as in the preceding three questions.

Compared to the original situation, how does this change affect current I1?

(a)   I1 remains the same.
(b)   I1 increases.
(c)   I1 decreases.

### QUESTION 5*

Two resistors are made from wire of resistivity ρ and cross sectional area A. The first resistor, R1, is made of a single wire of length L. The second resistor, R2, is made by connecting two parallel wires of length 4L together side-by-side as shown. What is the relation between R1 and R2?

(a)   R2 = R1
(b)   R2 = 2R1
(c)   R2 = 4R1

### QUESTION 6**

Two infinitely long current carrying wires run into the page as indicated. Consider a closed triangular path that runs from point 1 to point 2 to point 3 and back to point 1 as shown.

Which of the following plots best shows B·dl as a function of position along the closed path?

(a)
(b)
(c)

### QUESTION 7*

This question and the next two pertain to the circuit shown here.

The capacitor is initially uncharged and the switch is moved to position A at time t = 0.

What is the current I1 through resistor R1 immediately after the switch is moved to position A?

(a)   0.1 A
(b)   0.5 A
(c)   1.0 A
(d)   1.5 A
(e)   2.0 A

### QUESTION 8**

Determine the energy U stored in the capacitor after the switch has been at position A for a very long time.

(a)   0 mJ
(b)   0.125 mJ
(c)   0.250 mJ
(d)   0.500 mJ
(e)   1.000 mJ

### QUESTION 9*

After being at position A for a long time, the switch is now moved to position B. After the switch is moved to B, how much time does it take to reduce the charge on the capacitor to half of its original value?

(a)   0 μs
(b)   12.7 μs
(c)   50.0 μs
(d)   69.3 μs
(e)   100.0 μs

### QUESTION 10*

A magnetic field, B= 0.8 T, is directed out of the page in a region containing a rectangular up-side-down "U-wire" having width W = 0.5 m, as shown. A resistor of mass m and resistance R = 6 Ω, which is free to slide without friction on the vertical rails, is released from rest and starts falling in the presence of the earth's gravitational field, reaching a terminal speed v = 3.8 m/s.

What is the direction of the induced current in the loop formed by the resistor and the U-wire?

(a)   clockwise
(b)   counterclockwise

### QUESTION 11**

What is the mass of the resistor?

(a)   3.8 g
(b)   4.3 g
(c)   7.7 g
(d)   10.3 g
(e)   18.9 g

### QUESTION 12*

Which statement(s) below is (are) valid during the time the resistor is falling at terminal velocity?

(a)   The work per unit time done by the earth on the resistor is equal to the power dissipated in the resistor.

(b)   The work done by the magnetic field on the resistor is equal in magnitude, but opposite in sign, to the work done by the earth on the resistor.

(c)   Both of the statements above are valid.

### QUESTION 13*

This question and the next one pertain to this situation:

Consider a long wire running in the vertical direction with a rectangular loop of wire beside it as shown. Which of the following situations would result in a clockwise induced current in the loop?

(a)   A current in the long wire, directed upward, is increasing in magnitude.

(b)   With a constant current in the long wire directed upward, the loop is moved toward the top of the page, parallel to the long wire.

(c)   The loop is held stationary and the long wire, while carrying a constant upward current, is moved away from the loop.

### QUESTION 14**

Now suppose that a constant current, I, flows upward along the long wire, and the same magnitude current, I, flows clockwise in the loop. As viewed from the top of the page, in which direction does the loop rotate?

(a)   clockwise
(b)   counterclockwise
(c)   The loop does not rotate.

### QUESTION 15**

This question and the next one pertain to this situation:

A short, straight wire segment of length l carries current I and is oriented so that it makes an angle of 30° with the horizontal. Point P is a distance r below the wire segment.

Which expression below is the best approximation for the magnetic field caused by the wire segment at point P?

(a)   (μoIlcos30°) / (4π2)
(b)   (μoIlsin30°) / (4π2)
(c)   (μoIl) / (4π2)

### QUESTION 16*

Which direction depicted at right best describes the direction of the magnetic field at point P due to the wire segment?

(a)
(b)
(c)

### QUESTION 17**

This question and the next two refer to this figure:

A long, thin wire carrying constant current I = 2 A into the page is surrounded by a concentric cylindrical hollow wire of inner radius a = 0.12 m, and outer radius b = 0.26 m, carrying total current I = 4 A directed out of the page, as shown. Assume the current in the cylindrical hollow wire is distributed uniformly over its cross-sectional area.

At what radius is B = 0 in the region a < r < b inside the hollow wire?

(a)   0.19 m
(b)   0.20 m
(c)   0.21 m
(d)   0.25 m
(e)   The magnetic field is not zero anywhere inside the hollow wire.

### QUESTION 18***

Which one of the following statements is valid?

(a)   For radii r > b, the magnetic field is the same as the field a distance r from the center of a long wire carrying total current of 6 A directed out of the page.

(b)   Ampere's law is valid only in highly symmetric situations, such as the situation depicted in the diagram
.
(c)   The magnetic field at the point labeled C is directed out of the page.

(d)   The magnitude of the magnetic field at r = a is less than the magnitude of the magnetic field at point C (assume that the distance from the center to point C is 3a).

(e)   None of the statements above is valid.

### QUESTION 19**

This question and the next two refer to this situation:

A passenger jet is flying over Alaska in level flight at a constant altitude h = 10 km and constant speed of v = 300 m/s, immersed in the earth's vertically downward-pointing magnetic field of B = 30 μT. The distance between the tips of the aircraft's metal wings is d = 50 m.

Calculate the potential difference ε between the aircraft's wing tips due its motion through the earth's magnetic field.

(a)   ε = 0.0 volts
(b)   ε = 0.45 volts
(c)   ε = 0.90 volts

### QUESTION 20**

Which wingtip has positive charge, as viewed by a passenger in the airplane who is facing in the direction that the airplane is traveling?

(a)   the right wingtip
(b)   the left wingtip
(c)   neither wingtip

### QUESTION 21**

As shown in the figure below, a proton moves in the +x direction with speed v and is immersed in both, a uniform magnetic field, B, oriented in the -z direction, and a uniform electric field, E (not shown in the diagram). What electric field orientation is required in order for the proton to move un-deflected through the combined magnetic and electric field region?

(a)   +y direction
(b)   -y direction
(c)   +z direction

### QUESTION 22*

As shown in the figure below, a proton of mass m = 1.67 × 10-27 kg is initially moving in the +x direction with speed v = 3 × 105 m/s but then at x = 0, it abruptly encounters a region of space with uniform magnetic field of strength B = 5 μT oriented in the -z direction. How deep into this magnetic field region does the proton penetrate before being reflected backwards out of it?

(a)   d = 68.9 m
(b)   d = 257.3 m
(c)   d = 453.6 m
(d)   d = 626.3 m
(e)   d = 1738.9 m

### QUESTION 23*

A long thin wire of length L = 1 m carries a steady current, I = 3.0 A, and is immersed in a uniform magnetic field region of initially unknown strength B and initially unknown orientation. A UIUC Physics 212 student systematically orients the wire at various angles in space and finds that the net magnetic force acting on the wire has a maximum value of  F = 1.50 N along the +x direction, which occurs when the current I flowing in the wire is oriented in the +y direction. From this measurement, the P212 student deduces that the magnetic field strength, B, and its orientation in space is:

(a)   B = 0.5 T, in the +x direction
(b)   B = 0.5 T, in the -z direction
(c)   B = 0.5 T, in the +z direction
(d)   B = 1.5 T, in the -y direction
(e)   B = 1.5 T, in the +z direction

### QUESTION 24*

As shown in the figure, a short coil of radius a = 0.1 m and N = 100 turns of wire lies centered in the x-y plane and has a steady current I = 3.0 A flowing counter-clockwise through it. The vector magnetic dipole moment m of this coil is:

(a)   m = 0.094 A-m2, in the -z direction
(b)   m = 0.094 A-m2, in the +z direction
(c)   m = 9.42 A-m2, in the -z direction
(d)   m = 9.42 A-m2, in the +z direction
(e)   m = 94.2 A-m2, in the +z direction

### QUESTION 25*

As shown in the figure below, a square conducting loop of side a = 0.1 m carries a steady current I = 4.0 A circulating in a counter-clockwise direction. An external, uniform magnetic field of strength B = 0.5 T is oriented along the +z direction, making an opening angle of Θ = 30° with the unit normal n of the square conducting loop. The magnitude of the torque, τ , and the potential energy, U, associated with the external magnetic field B interacting with the loop's magnetic dipole moment m are:

(a)   τ = 0.010 A-m2, U = -0.017 J
(b)   τ = 0.010 A-m2, U = 0.017 J
(c)   τ = 0.017 A-m2, U = 0.010 J
(d)   τ = 0.017 A-m2, U = -0.010 J
(e)   τ = 0.017 A-m2, U = -0.017 J

### QUESTION 26*

A long, straight wire of radius a carries a steady current I = 2.0 A. The graph of magnetic field strength B(r) as a function of perpendicular distance r from the center of the wire is:

(a)
(b)
(c)

### QUESTION 27**

As shown in the figure below, a circular loop of radius a = 0.1 m lies in the horizontal x-y plane with its center located at the origin, with steady current I = 2.0 A circulating in a counter-clockwise direction in the loop. The magnetic field strength B(0,0,z) at the observation point (x, y, z) = (0, 0, 0.1 m) and its direction, due to the current I flowing in the circular loop is:

(a)   B(0,0,z=0.1m) = 0.628 × 10-7 T, -z direction
(b)   B(0,0,z=0.1m) = 2.323 × 10-6 T, +z direction
(c)   B(0,0,z=0.1m) = 3.678 × 10-6 T, -z direction
(d)   B(0,0,z=0.1m) = 4.443 × 10-6 T, +z direction
(e)   B(0,0,z=0.1m) = 8.886 × 10-6 T, +z direction

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.