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 120. The exam period was 90 minutes; the mean was 92.0; the median was 96. Click here to see page1 page2 of the formula sheet that came with the exam.

This circuit has three batteries with voltages V_{1}, V_{2} and V_{2}, three standard resistors of resistance R_{1} and a light bulb with resistance R_{2}.

Which one of the choices listed on the right is an expression for the magnitude of the current I in terms of V_{1}, V_{2}, R_{1} and R_{2}?

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

(a) lower than (b) the same as (c) higher than

Three resistors, three capacitors, a battery and two switches are connected in the circuit shown below. The values of all circuit elements are given in the figure. Originally, the switches S_{1} and S_{2} are open (as shown) and all of the capacitors are uncharged. At time t = 0, both switches are closed.

What is the current I_{1} through resistor R_{1} immediately after the switches are closed?

(a) I_{1} = 0 A (b) I_{1} = 1.8 A (c) I_{1} = 2.5 A (d) I_{1} = 3.8 A (e) I_{1} = 4.7 A

(a) I_{2} > 0 (b) I_{2} = 0 (c) I_{2} < 0 (i.e. opposite the direction shown)

(a) Q_{2} = 0 μC (b) Q_{2} = 33 μC (c) Q_{2} = 90 μC (d) Q_{2} = 180 μC (e) Q_{2} = 270 μC

(a) t_{1/e} = 1200 μsec (b) t_{1/e} = 1500 μsec (c) t_{1/e} = 3000 μsec (d) t_{1/e} = 3600 μsec (e) t_{1/e} = 4800 μsec

An electron of mass m and charge q is accelerated to the right (in the plane of the page) from rest through a potential difference V. The electron then enters a region, defined by x > 0, containing a uniform magnetic field.

When the electron enters the region with the magnetic field the force on it is directed

(a) toward the top of the page. (b) toward the bottom of the page. (c) into the page.

(a) increases. (b) decreases. (c) remains constant.

(a) T = 1.2 × 10^{-15} s (b) T = 7.5 × 10^{-12} s (c) T = 6.0 × 10^{-11} s (d) T = 8.3 × 10^{-8} s (e) T = 4.1 × 10^{-5} s

A rectangular wire loop of height h and width w, centered on the origin, carries current I in the direction shown in the figure. The angle between the positive x-axis and the plane of the loop is θ, defined as shown in the figure below. (When θ = 0 the loop lies in the x-z plane.) This entire region of space is filled with a uniform external magnetic field B pointing in the +x direction.

When θ = 60°, the force on the leg of length h with the upward-going current is in the

(a) positive x direction. (b) negative x direction. (c) positive y direction. (d) negative y direction. (e) positive z direction

(a) |W| = 9.09 × 10^{-5} J (b) |W| = 2.37 × 10^{-4} J (c) |W| = 4.25 × 10^{-4} J (d) |W| = 5.87 × 10^{-4} J (e) |W| = 8.13 × 10^{-4} J

(a) does no work on the loop. (b) does positive work on the loop. (c) does negative work on the loop.

What is the direction of the torque on the wire carrying I_{1} due to the current I_{2} in the other wire?

(a) in the positive y direction (b) in the positive z direction (c) in the negative y direction

A solid, infinitely-long, conducting rod has radius a = 15 cm and lies along the z axis. It carries a current I = 30 A in the +z direction. The current is uniformly distributed across the rod. It is surrounded, at a distance b = 30 cm, by a thin coaxial conducting shell that carries a current of the same magnitude, but directed in the -z direction.

Find the magnitude B of the magnetic field at a distance of 10 cm from the origin.

(a) B = 2.67 × 10^{-5} T (b) B = 3.52 × 10^{-5} T (c) B = 4.80 × 10^{-5} T (d) B = 6.15 × 10^{-5} T (e) B = 7.20 × 10^{-5} T

(a) negative x direction (b) negative y direction (c) positive y direction

A rectangular wire loop of height h, width w and net electrical resistance R lies in the x-y plane. As shown in the figure below, there is a region of space at -1.5w < x < 0 in which there is a magnetic field pointing in the -z direction. In order to determine the magnitude of this field, a student pulls the wire loop through the magnetic field region at a constant velocity v in the +x-direction, and measures the current I induced in the loop during this process.

If, when the leading edge, A, of the loop is located at x_{A} = -w, the student measures a current of 20 × 10^{-6} amps, what is the magnitude B of the magnetic field?

(a) B = 0.12 T (b) B = 0.31 T (c) B = 0.57 T (d) B = 0.99 T (e) B = 1.15 T

(a) clockwise (b) counter-clockwise (c) No current flows in the loop in this situation.

The figure at right shows a circular wire loop of total resistance R. The loop is contained within a region having a uniform magnetic field B pointing out of the page, and is attached to a motor that keeps it rotating around the y-axis in a clockwise direction (when looking in the negative y-direction) at constant angular velocity ω. The loop is initially parallel to the x-y plane (the plane of the paper), as shown.

Which one of the following graphs best represents the EMF induced in the loop as a function of time? (ε changes sign if the induced current changes direction; ε = 0 is denoted on the graphs. In the initial (t = 0) position shown in the figure above, ε is defined to be positive if it leads to clockwise current in the loop).

(a) |ε| = 0 V (b) |ε| = 0.0563 V (c) |ε| = 0.125 V (d) |ε| = 0.224 V (e) |ε| = 0.418 V

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

Three identical resistors are connected to a battery, an inductor, and a switch as shown in the figure. (The values of all circuit elements are given below the figure.) The switch has been open for a very long time, and then it is closed at time t = 0.

Calculate the current delivered by the battery immediately after the switch is closed.

(a) 0.353 A (b) 0.706 A (c) 0.998 A (d) 1.22 A (e) 1.38 A

(a) V_{L} = 0 V (b) V_{L} = 6 V (c) Neither of the above answers is correct.

(a) E_{L} = 3.30 × 10^{-6} J (b) E_{L} = 5.62 × 10^{-6} J (c) E_{L} = 8.63 × 10^{-6} J (d) E_{L} = 1.07 × 10^{-5} J (e) E_{L} = 1.12 × 10^{-5} J

(a) f_{I} = 0.0521 (b) f_{I} = 0.0926 (c) f_{I} = 0.158 (d) f_{I} = 0.201 (e) f_{I} = 0.236