### Spring 2011 Physics 102 Hour Exam 2(28 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 115. The exam period was 90 minutes; the mean score was 87.8; the median was 90. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

• A reminder about prefixes: p (pico) = 10-12; n (nano) = 10-9; μ (micro) = 10-6; m (milli) = 10-3; k (kilo) = 10+3; M or Meg (mega) = 10+6; G or Gig (giga) = 10+9.

### QUESTION 1*

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

A proton enters a magnetic field of magnitude 4.7 T directed into the page. When an external electric field of 300 N/C, directed downward, is applied, the proton travels in a straight line.

What is the speed of the proton?

(a)   1.2 ×10-2 m/s
(b)   3.5 m/s
(c)   47.0 m/s
(d)   63.8 m/s
(e)   126 m/s

### QUESTION 2***

Suppose the proton were replaced by an electron. Which direction would the electric field have to point for the electron to travel in a straight line?

(a)   up
(b)   down

### QUESTION 3**

Three long current-carrying wires are arranged as shown in the diagram. Point P is halfway between the first and second wires. Calculate the magnetic field at point P.

(a)   1.24 × 10-5 T out of the page
(b)   4.10 × 10-5 T out of the page
(c)   8.10 × 10-5 T out of the page
(d)   4.10 × 10-5 T into the page
(e)   1.24 × 10-5 T into the page

### QUESTION 4*

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

A rectangular loop of sides a = 6.75 cm and b = 12 cm is sitting in a magnetic field of strength B = 5 mT, as shown in the diagram. A current of 6 A flows through the loop. The normal to the loop makes an angle of 70° with respect to the magnetic field. Calculate the torque on the loop.

(a)   τ =1.88 × 10-4 Nm
(b)   τ = 2.28 × 10-4 Nm
(c)   τ = 2.43 × 10-4 Nm

### QUESTION 5**

In which direction does side a of the loop move in response to the torque?

(a)   up
(b)   down

### QUESTION 6**

An experiment is done to levitate a piece of current-carrying wire in a magnetic field. The wire available is 5-gauge copper wire, which has a cross-sectional diameter of 4.62 mm and a mass density of 8930 kg/m3. The maximum current allowed through the wire is 118 A. The minimum magnetic field necessary to achieve this levitation is:

(a)   B = 0.004 T
(b)   B = 0.012 T
(c)   B = 0.049 T
(d)   B = 0.121 T
(e)   B = 0.367 T

### QUESTION 7**

A wire carrying current I is placed in a magnetic field which is oriented parallel to the current. The wire will experience a non-zero force.

(T)   True
(F)   False

### QUESTION 8**

Consider a loop rotating with constant angular frequency ω in a uniform magnetic field. Which of the following statements is TRUE?

(a)   When the flux through the loop is at a maximum, the induced EMF is zero.
(b)   When the flux through the loop is zero, the induced EMF is zero.
(c)   The induced EMF does not depend on the area of the loop.

### QUESTION 9***

This graph shows how the flux through a stationary loop varies in an interval of time.

Which one of the following statements is FALSE?

(a)   The current in the loop switches directions after a period of time.
(b)   The induced EMF in the loop is never zero.
(c)   The magnetic field through the loop is always increasing.

### QUESTION 10*

This question and the next one pertain to the same situation.

A solenoid has a diameter of 1 cm and a length of 20 cm. If it has an inductance of 3 μH, how many loops of wire make up this solenoid?

(a)   26
(b)   39
(c)   78
(d)   1520
(e)   6100

### QUESTION 11*

The solenoid is now connected to a battery. After a long time, the current through solenoid settles to I = 2 mA. How much energy is stored in the inductor?

(a)   6.0 × 10-12 J
(b)   7.8 × 10-11 J
(c)   1.4 × 10-10 J

### QUESTION 12**

This question and the next two deal with the situation described below.

A rectangular coil of dimensions 4 cm x 3 cm and with 20 turns is being pulled into and through a region of uniform magnetic field of 2 T at a speed of 3 m/s.

Just after the left side of the coil enters the magnetic field region, what is the magnitude of the induced EMF?

(a)   0 V
(b)   0.34 V
(c)   0.0024 V
(d)   3.6 V
(e)   4.8 V

### QUESTION 13**

From the perspective given in the drawing, what is the direction of the induced current?

(a)   There is no current.
(b)   clockwise
(c)   counterclockwise

### QUESTION 14**

If the clockwise direction is considered the positive direction of current, which sketch most closely resembles the EMF as the loop is dragged into, through, and out of the field?

(a)
(b)
(c)

### QUESTION 15**

A transformer has a primary rms voltage of 110 V. The secondary is connected to a 72 Ω resistor. Enough wire exists to make a total of 100 loops in the primary and secondary combined. What should the ratio Np:Ns be such that the average power dissipated by the resistor is 75 W?

(a)   70:30
(b)   60:40
(c)   50:50
(d)   40:60
(e)   30:70

### QUESTION 16*

This question and the next three are related.

In the RLC circuit shown above, a function generator provides an AC voltage of amplitude V0 = 120 V at a frequency f = 60 Hz. The components in the circuit have values R = 30.0 Ω, L = 200 mH and C = 20.0 μF.

What is the phase angle between the current and the AC source?

(a)   -85.5°
(b)   -62.3°
(c)   0.12°
(d)   40.2°
(e)   73.8°

### QUESTION 17*

What is the maximum current that flows through the circuit with these parameters?

(a)   0.400 A
(b)   0.571 A
(c)   0.929 A
(d)   1.06 A
(e)   1.86 A

### QUESTION 18*

The capacitor in the circuit is now replaced such that the circuit is at resonance. What is the new capacitance?

(a)   1.22 μF
(b)   5.41 μF
(c)   11.2 μF
(d)   35.2 μF
(e)   48.0 μF

### QUESTION 19**

At resonance, what is the average power dissipated in the circuit?

(a)   50 W
(b)   120 W
(c)   180 W
(d)   240 W
(e)   300 W

### QUESTION 20**

When does Kirchoff's loop rule hold true?

(a)   in DC circuits only
(b)   only when the current is at its maximum value
(c)   in all circuits at every instance of time

### QUESTION 21**

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

Consider a circular conducting loop of diameter d = 10 cm placed in a uniform magnetic field B. The magnetic field B(t) changes in time as shown in the plot to the right. Note: in this plot, a positive value for B(t) corresponds to a field directed into the page.

What is the direction of the current around the loop at time t = 5 s?

(a)   clockwise
(b)   counterclockwise

### QUESTION 22*

Calculate the magnitude of the EMF |ε| in the loop at the same time t = 5 s.

(a)   0 mV
(b)   0.78 mV
(c)   1.45 mV
(d)   20.6 mV
(e)   643 mV

### QUESTION 23**

At which of the following time points is the magnitude of the EMF |ε| largest?

(a)   t = 5 s
(b)   t = 12 s
(c)   t = 20 s

### QUESTION 24*

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

A rectangular loop of sides a = 2 cm and b = 3 cm has N = 32 turns. The loop carries a current of 2.7 A. The surface normal makes an angle θ with the z-axis. A uniform external magnetic field of B = 2.0 tesla points in the positive z direction. The torque on the loop is 0.072 Nm. Calculate the angle θ.

(a)   16°
(b)   25°
(c)   32°
(d)   39°
(e)   44°

### QUESTION 25*

A square loop with sides L = 2.45 cm and 32 turns is placed in this B field at the same angle θ and current. What is the ratio of the torque on the square loop to the torque on the rectangular loop?

(a)   τsquare / τrectangle  =  0.82
(b)   τsquare / τrectangle  =  1.00
(c)   τsquare / τrectangle  =  1.22

### QUESTION 26*

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

A beam of particles with same mass m and same velocity v = 9000 m/s but with different charges q1, q2 and q3 is sent into a uniform magnetic field B = 0.8 T that is pointing out of the page. The situation is sketched here.

The magnetic field does a larger work on charge q2 than on charge q1.

(T)   True
(F)   False

### QUESTION 27*

When comparing the charges q1, q2 and q3 the following can be stated (remember to consider the sign of the charge):

(a)   q1 > q2 > q3
(b)   q2 > q1 > q3
(c)   q3 > q1 > q2

### QUESTION 28*

If the radius of the circular trajectory of q1 is r1 = 0.69 mm and q1 = 3e (where e = 1.6 × 10-19C), what is the mass of the particles?

(a)   1.67 × 10-27 kg
(b)   2.94 × 10-26 kg
(c)   3.69 × 10-26 kg

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.