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 117. The exam period was 90 minutes; the mean score was 95.5; the median was 99. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

Some helpful information: • 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}.

(a) resistor (b) capacitor (c) inductor (d) capacitor and inductor (e) inductor and resistor

I) V_{gen}(t) = V_{L}(t) + V_{R}(t) + V_{C}(t) II) V_{gen,max} = V_{L,max} + V_{R,max} + V_{C,max}

(a) I (b) II (c) I and II

(a) 130 (b) 156 (c) 3900 (d) 4680 (e) none of the above

The phasor diagram for a series RLC circuit is shown here with phasors V_{R}, V_{L} and V_{C} corresponding to the resistor, capacitor, and inductor, respectively. Three additional phasors (A, B, and C, in dotted lines) are included as well.

Which of these three phasors corresponds to that of the generator?

(a) A (b) B (c) C

(a) The frequency is less than the resonant frequency. (b) The frequency is the same as the resonant frequency. (c) The frequency is greater than the resonant frequency.

If the current in the central loop is increased, in what directions will induced currents in the top loop and the bottom loop flow?

(a) Top - counterclockwise; Bottom - counterclockwise (b) Top - counterclockwise; Bottom - clockwise (c) Top - clockwise; Bottom - counterclockwise (d) Top - clockwise; Bottom - clockwise (e) There are no induced currents.

Assuming that all particles have the same speed, what is the ratio R_{235} / R_{238} of the radii of the paths taken by the two isotopes?

(a) 0.987 (b) 1.217 (c) 2.090

What is the phase angle φ associated with the generator?

(a) -12° (b) 27° (c) 41° (d) 67° (e) 72°

A charged particle travels through two chambers as shown below. It enters Chamber 1 from below and exits Chamber 2 from above. The particle moves at a speed of 150 m/s. The magnetic field in Chamber 2 has a magnitude of 0.8 T.

Assuming the particle is negatively charged, what is the direction of the magnetic field in Chamber 1?

(a) into the page (b) out of the page (c) to the right

(a) 2.22 C (b) 3.49 C (c) 6.98 C (d) 2220 C (e) 3490 C

(a) B_{1} > B_{2} (b) B_{1} = B_{2} (c) B_{1} < B_{2}

As shown below, an RLC circuit consists of a resistor R, a variable capacitor C, an inductor L and an AC power source generating a voltage of V(t) = V_{0} sin(2π f t). Circuit parameters R, L and V_{0} are fixed at R = 50 Ω, L = 4 mH and V_{0 }= 20 V, and the generator frequency is set to f = 5 kHz.

To what value should you change the capacitance C for the circuit to be in resonance with the frequency f of the generator?

(a) 2.5 × 10^{-7} F (b) 7.5 × 10^{-3} F (c) 8.3 F

(a) 0.5 watts (b) 1 watt (c) 4 watts (d) 16 watts (e) 256 watts

(a) 19 Ω (b) 57 Ω (c) 112 Ω (d) 294 Ω (e) 1061 Ω

(a) L_{2} = L_{1} / 4 (b) L_{2} = L_{1} / 2 (c) L_{2} = L_{1} (d) L_{2} = 2 L_{1} (e) L_{2} = 4 L_{1}

A circular loop is placed in a uniform external magnetic field B pointing into the page. The loop has resistance R.

The external magnetic field B is turned up slowly at a constant rate from 0 to 1 T in 100 s. Is there a current in the loop, and if so, in which direction does it flow?

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

(a) ε is 100 times smaller. (b) ε is 10 times smaller. (c) ε is the same. (d) ε is 10 times larger. (e) ε is 100 times larger

In the circuit shown below the resistor has a resistance of 5 Ω. The solenoid has 7 turns, a length of 10 cm and a radius of 1 cm. The battery supplies 10 volts to the circuit. Assume the battery has been connected for a long time.

Determine the value of the magnetic field B inside the solenoid after a time long enough for the circuit to achieve its maximum current.

(a) B = 2.70 × 10^{-7} T (b) B = 9.34 × 10^{-5} T (c) B = 1.76 × 10^{-4} T (d) B = 3.33 × 10^{-2} T (e) B = 0.29 T

(a) 1.97 × 10^{-7} H (b) 0.87 × 10^{-6} H (c) 3.24 × 10^{-4} H (d) 7.97 × 10^{-4} H (e) 2.21 × 10^{-3} H

A rectangular loop of dimensions 3 cm × 5 cm is initially in a region having a uniform magnetic field of B = 3 T. The loop is being pulled out of this region into a region of no field at a rate of v = 10 m/s.

Consider a time interval beginning when the loop is well within the region of the magnetic field and ending when it is well into the field-free region. Over this interval, as a function of time, which graphs best represent the magnetic flux Φ and the induced EMF ε in the loop?

(a) I (b) II (c) III

Consider an instant during which the loop is partly out of the field region as shown above. If the resistance of the loop is 2 Ω, what is the magnitude of the current generated in the loop?

(a) 0.003 A (b) 0.45 A (c) 6.25 A (d) 34 A (e) There is no current generated.

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

A single square loop of wire of side 0.2 m lies in the x-y plane. A current I = 3 A flows around the loop in a clockwise direction, as shown in the figure. A uniform magnetic field B of magnitude 0.75 T points along the +x direction.

What is the magnitude of the torque τ on the loop due to the magnetic field?

(a) τ = 0.039 N·m (b) τ = 0.063 N·m (c) τ = 0.090 N·m

(a) 1 (b) 2 (c) 3 (d) 4 (e) The loop does not rotate.

(a) 0 N·m (b) 0.024 N·m (c) 0.056 N·m

(a) M = 0.038 μH (b) M = 0.27 μH (c) M = 1.4 μH