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 131. The exam period was 90 minutes; the mean score was 94.5; the median was 97. Click here to see page1 page2 of the formula sheet that came with the exam.

In a region of space there is a constant magnetic field as shown in the shaded part of the figure below. A square loop of side L = 0.1 m and resistance R = 12 Ω is moved at constant velocity of 0.1 m/s in the direction indicated by the arrow. The magnetic field extends for a length L = 0.1 m in the direction of motion. In the figure below, which of the waveforms best describes the current in the loop as a function of time?

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

(a) I = 0.1 mA (b) I = 2 mA (c) I = 0.5 mA (d) I = 1 A (e) I = 1 mA

What is the torque on the loop at the position shown in the figure (torque = F r sinα)?

(a) torque = 0.084 Nm (b) torque = 3.5 Nm (c) torque = 0 Nm (d) torque = 0.21 Nm (e) torque = 0.168 Nm

In a region of space of width L = 0.1 m there is a magnetic field B = 0.25 T pointing into the page as shown in the figure. A 1 mg particle with speed v and charge Q = -2 mC enters the region of the magnetic field along the line indicated in the figure. Ignore gravity in this problem. (Note that Q is negative.)

What is the direction of the force on the particle when the particle enters the region of the magnetic field?

(a) +z (up out of the page) (b) -z (down into the page (c) +y (d) -y (e) +x

(a) v = 10^{5} m/s (b) v = 50 m/s (c) v = 5000 m/s (d) v = 250 m/s (e) v = 2000 m/s

(a) same as v (b) greater than v (c) less than v

A circular loop of radius r = 5 cm and resistance R = 0.10 Ω is in a region where there is a uniform magnetic field in the direction shown in the figure that increases linearly with time according to the expression

B(t) = B_{0} t / τ

What is the direction of the current in the loop (choose between a and b arrows as indicated in the figure [front view])?

(a) (b)

(a) I = 0 (b) I = 0.34 mA (c) I = 0.39 mA (d) I = 0.2 mA (e) I = 3.4A

An ideal transformer with 5 turns on the primary and 10 turns on the secondary is shown in the figure. A sinusoidal voltage source having V(t) = 10 sin(ωt) [in volts] is connected across the primary and a 1 Ω resistor is connected across the secondary. ω = 100 rad/s.

What is the maximum value of the voltage in the secondary circuit?

(a) 5 volts (b) 10 volts (c) 20 volts

(a) 2.0 Amp (b) 5.0 Amp (c) 10.0 Amp (d) 20.0 Amp (e) 40.0 Amp

(a) doubles (b) halves (c) stays the same

An alternating voltage source of 10 volts (rms) at 60 Hz is applied to a circuit depicted below. The capacitor C = 100 μF. What is the rms value of the current through the resistor R?

(a) 0 (b) 0.26 A (c) 0.46 A (d) 0.65 A (e) 2.15 A

(a) 50° (b) 62° (c) 72° (d) 42° (e) 32°

(a) zero (b) 90° (c) 180°

A coil of 22 turns and length 40 cm is connected to a voltmeter. A time-dependent magnetic field is generated by a moving magnet nearby.

The average magnetic flux inside the coil as a function of timefor (t < 0.1s) is given by the expression

Φ(t) = (2 - t / 0.05s) 10^{-4} T m^{2}

(See figure below.)

What is the induced EMF of the coilfor 0 < t < 0.1?

(a) 0.33 volts (b) 0.22 volts (c) 0.11 volts (d) 0.044 volts (e) 0.022 volts

(a) 0.132 volts (b) 0.248 volts (c) 0.396 volts (d) 2.48 volts (e) 1.32 volts

(a) the same (b) twice as big (c) half

What is the resonant frequency of this RLC circuit?

(a) 312.5 radians/sec = 49.7 Hz (b) 158.1 radians/sec = 25.2 Hz (c) 17.7 radians/sec = 2.8 Hz

(T) True (F) False

(a) I = 0 (b) I = 0.028 A (c) I = 0.333 A (d) I = 0.500 A (e) I = ∞

An unpolarized electromagnetic wave is incident on a series of three linear polarizers, each with the polarization angle rotated at 45° with respect to the previous one.

If the initial intensity of the unpolarized light is I_{0}, what is the intensity I_{1} transmitted through the first polarizer?

(a) I_{1} = I_{0} / 4 (b) I_{1} = I_{0} / 2 (c) I_{1} = I_{0}

(a) only the electric field is reduced. (b) only the magnetic field is reduced. (c) both the electric and magnetic field are reduced.

(a) I_{3}_{ }= 0 (b) I_{3}_{ }= I_{1} / 2 (c) I_{3}_{ }= I_{1} / 4 (d) I_{3}_{ }= I_{1} / 8 (e) I_{3}_{ }= I_{1} / 16

(a) the speed of sound at an altitude of 36,000 feet (b) one billion feet per second (c) the orbital speed of the space shuttle (d) the circumference of the earth's orbit divided by 365 days (e) one trillion meters per second

A current of 5 A passes through a solenoid of length L = 30 cm and diameter 5 cm. The number of turns of the solenoid is 250.

What is the value of the magnetic field inside the solenoid?

(a) 15.2 mT (b) 5.2 mT (c) 1 T (d) 12.56 mT (e) 0 T

(a) 4.57 J (b) 10.7 J (c) 6.42 mJ (d) 200 J (e) 2.176 mJ

(a) 3.3 m (b) 102.7 m (c) 2.7 × 10^{15} m

When it sent the 575 nm signal, the starship was moving

(a) away from Earth. (b) towards Earth.