### Spring 2010 Physics 102 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 111. The exam period was 90 minutes; the mean score was 75.6; the median was 77. 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***

A particle with charge 1 C and mass 1 kg moves in a uniform magnetic field of magnitude 1 T pointing in the positive z direction. The initial velocity components of the particle are vx = 1 m/s, vy = 2 m/s and vz = 3 m/s. What is the subsequent motion of the particle?

(a)   moves in a circle at the initial speed
(b)   moves in a helix along the initial direction with radius 3.7 m
(c)   moves in a helix along the initial direction with radius 2.2 m
(d)   moves in a helix along the z direction with radius 3.7 m
(e)   moves in a helix along the z direction with radius 2. m

### QUESTION 2*

Two parallel wires have current flowing through them in opposite direction. The two wires will

(a)   attract each other.
(b)   repel each other.
(c)   not exert force on each other.

### QUESTION 3***

The transformer below has an iron core with a primary coil consisting of 10 windings. The secondary coil has 5 windings. The primary coil is on the left side of the figure.

A DC voltage of 12 V is applied to the primary coil. What is the expected amplitude of Vout?

(a)   24 V
(b)   12 V
(c)   6 V
(d)   3 V
(e)   0

### QUESTION 4*

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

A square loop consisting of 10 turns with sides equal to 1 cm carrying a current of 2 A is situated at the center of a solenoid with 100 turns per meter. The normal to the square loop is tilted at an angle 30° from the solenoid's longitudinal axis. What is the magnitude of the torque on the loop when a current of 3 A passes through the solenoid?

(a)   1.9 × 10-7 N-m
(b)   3.8 × 10-7 N-m
(c)   4.4 × 10-7 N-m
(d)   3.8 × 10-5 N-m
(e)   4.4 × 10-5 N-m

### QUESTION 5**

In the previous question, the current in the square loop is now turned off. With the solenoid current still flowing, the loop is now mechanically rotated with angular frequency ω about the axis perpendicular to both the solenoid's axis and the normal to the square loop. What is the value of ω if the maximum current generated in the loop is 2 A? Assume the total resistance of the loop is 0.001 Ω.

(a)   5.3 × 10-3 rad/s
(e)   1.3 × 105 rad/s

### QUESTION 6**

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

An electron travels in a straight line in the presence of constant electric and magnetic fields.

How are the electric and magnetic fields aligned?

(a)   perpendicular to each other
(b)   parallel to each other
(c)   with a 45° angle between two vectors

### QUESTION 7*

The magnitude of the electric field is 5 N/C, and that of magnetic field is 10 T. What is the speed of the electron?

(a)   2 m/s
(b)   50 m/s
(c)   5 m/s
(d)   15 m/s
(e)   0.5 m/s

### QUESTION 8*

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

The electric load of a set of apartments can be represented by a resistor. The resistor is connected to a transformer, as shown in the diagram. The primary of the transformer is connected to the city's power distribution network, rated at Vpri-max = 13.2 kV, and the secondary is supplying Vsec-max = 230 V to the apartments. The frequency in this AC circuit is 60 Hz.

The primary coil of the transformer is made using Np = 26,400 turns. What is the number of turns of the secondary coil?

(a)   13200
(b)   110
(c)   460

### QUESTION 9**

The electric load is represented by a resistor with R = 0.2 ohms. What is the maximum current in the primary coil supplied by the city to the building?

(a)   20 A
(b)   115 A
(c)   1150 A
(d)   13200 A
(e)   264500 A

### QUESTION 10**

The transformer primary is only rated to handle 6.2 × 106 watts of peak power. What is the maximum attainable rms current in the transformer secondary, independent of the load R?

(a)   32 A
(b)   5600 A
(c)   19 kA

### QUESTION 11***

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

A square loop of wire of length 10 cm on a side and with resistance R = 2 Ω lies in the x-y, plane in a region of space containing a uniform magnetic field B pointing out of the page (in the z-direction). The magnetic field has a time dependence as shown in the graph, going to zero at t = 10 sec, and reversing direction for t > 10 sec.

What is the current in the loop at time t = 10 sec?

(a)   0 A
(b)   1 mA
(c)   2 mA
(d)   5 mA
(e)   10.0 mA

### QUESTION 12**

The EMF has a larger magnitude at t = 20 s than at t = 10 s.

(T)   True
(F)   False

### QUESTION 13*

This question and the next three are conceptually related.

A bar magnet falls from point A to point B through a solenoid with its ends connected. The solenoid is made of steel wire with resistance per unit length of 1 Ω/cm.

How does the speed of the magnet at point B compare to what it would be if the solenoid were not there?

(a)   It is greater.
(b)   It is less.
(c)   It stays the same.

### QUESTION 14*

Which picture best represents the EMF generated in the solenoid as a function of time when the magnet passes through it?

(a)
(b)
(c)

### QUESTION 15***

If the solenoid is made of copper wire, which has a smaller resistance per unit length than steel wire, how does the magnitude of the EMF generated in the solenoid change?

(a)   It is greater.
(b)   It is less.
(c)   It stays the same.

### QUESTION 16***

How does the speed of the magnet at point B with the copper solenoid compare to the case when the solenoid is made of steel?

(a)   It is greater.
(b)   It is less.
(c)   It stays the same.

### QUESTION 17*

This question and the next two are conceptually related.

In the first experiment a particle of mass m, charge q and velocity v enters a region with magnetic field B perpendicular to the plane of the paper. The particle performs a half circle trajectory and exits the region after time t at a distance d from the entrance point.

In the second experiment the particle has mass 2m. The charge, velocity and magnetic field stay unaltered. What distance from the entrance point will the particle exit the region?

(a)   2d
(b)   d
(c)   d / 2

### QUESTION 18***

In the third experiment the mass of the particle is again m, but the velocity v is doubled. After what time will the particle exit the region?

(a)   t
(b)   2t
(c)   t / 2

### QUESTION 19*

The charge of the particle is

(a)   positive.
(b)   negative.

### QUESTION 20**

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

A conducting rod of finite resistance and length L moves down frictionless vertical wires at a constant velocity v. The wires are connected across a capacitor. A uniform magnetic field B is present everywhere, pointing into the page as indicated.

Which plate of the capacitor is positively charged?

(a)   right one
(b)   left one

### QUESTION 21*

If v = 5 m/s, B = 0.5 T, L = 3 m and C = 6 μF, what charge is stored on the plates of the capacitor after a long time?

(a)   45 μC
(b)   18 μC
(c)   5.0 μC
(d)   3.2 μC
(e)   1.8 μC

### QUESTION 22*

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

An inductor is made from a wire-wound cylindrical solenoid of radius 2.5 mm, length 1 cm, and containing 1000 turns of wire. A current I = 50 mA flows through the wire.

Calculate the inductance L of the solenoid.

(a)   0.25 nH
(b)   2.5 μH
(c)   2.5 mH

### QUESTION 23*

How much energy is stored on the inductor?

(a)   0 μJ
(b)   3.1 μJ
(c)   62.5 μJ

### QUESTION 24**

A single loop of wire of radius R = 5 mm is centered around the inductor. Calculate the mutual inductance M of the inductor on the loop. (Recall that Φs = MIp.)

(a)   0.25 nH
(b)   2.5 nH
(c)   2.5 μH
(d)   25 μH
(e)   2.5 mH

### QUESTION 25*

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

A rectangular loop of wire lies in the x-y plane as shown below and it carries a current of 2.5 A. The sides a-b and c-d are parallel to the x-axis and are of length 6 cm while the sides a-d and b-c are of length 5 cm and parallel to the y-axis. The loop sits in a constant uniform magnetic field B.

Along what direction should the magnetic field be applied for the force on segment a-d to be zero, but for the force on a-b and the torque on the loop to be non-zero (Fad = 0, Fab ≠ 0, τ ≠ 0)?

(a)   along the x-axis
(b)   along the y-axis
(c)   along the z-axis
(d)   in the x-z plane at 45° to the z-axis
(e)   no such situation is possible

### QUESTION 26*

The magnetic field is 3 tesla and now oriented at 30° to the z-axis in the y-z plane. What is the torque on the loop?

(a)   16 N-m
(b)   3.7 N-m
(c)   0.235 N-m
(d)   0.011 N-m
(e)   0.007 N-m

### QUESTION 27**

Next the field of the same magnitude is oriented at 30° to the z-axis, but in the x-z plane. The torque

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

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.