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 was 94.1; the median was 98. Click here to see page1 page2 of the formula sheet that came with the exam.

The figure depicts a square wire coil with 4 loops. The length of each side of the square is L. The coil is situated in a region of constant magnetic field B = 0.2 T pointing in the +y direction. A current I = 20 amps flows in the coil in the direction shown (the black arrowhead indicates the current direction on the side of the square nearest you.) The square coil makes an angle of α with the xz-plane and the coil has a magnetic dipole moment with magnitude 25 A m^{2}.

What is the length of a side of the square loop?

(a) L = 0.44 m (b) L = 0.56 m (c) L = 0.62 m

(a) 2.5 N m (b) 3.3 N m (c) 4.1 N m (d) 4.6 N m (e) 5.0 N m

(a) clockwise (decreasing α) (b) counterclockwise (increasing α)

(a) α = 0° (b) α = 45° (c) α = 90°

(a) | ΔU | = 0.67 J (b) | ΔU | = 1.00 J (c) | ΔU | = 1.25 J (d) | ΔU | = 2.00 J (e) | ΔU | = 2.50 J

Two fixed conductors are connected by a resistor R = 20 Ω. The two fixed conductors are separated by L = 2.5 m and lie horizontally. A moving conductor of mass m slides on them at a constant speed v, producing a current of 3.75 amps. A magnetic field (shown by the black dots in the figure) with magnitude 5 T points out of the page.

In which direction does the current flow through the moving conductor when the bar is sliding in the direction shown?

(a) to the right (b) to the left

(a) v = 1 m/s (b) v = 3 m/s (c) v = 5 m/s (d) v = 6 m/s (e) v = 9 m/s

(a) F = 28 N (b) F = 37 N (c) F = 47 N

The values of all circuit elements are given in the figure. The capacitor is initially uncharged. Then, at time t = 0, the switch is closed.

What is the current through the battery immediately after the switch is closed?

(a) I = 0.6 A (b) I = 0.9 A (c) I = 1.2 A

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

(a) Q = 2.0 μC (b) Q = 3.0 μC (c) Q = 4.0 μC (d) Q = 5.0 μC (e) Q = 6.0 μC

(a) 2.4 μs (b) 3.3 μs (c) 6.7 μs (d) 10.0 μs (e) 30.0 μs

With the switch open, what is the current I_{1}? (A positive sign means that current flows in the direction of the arrow.):

(a) -0.20 A (b) -0.05 A (c) +0.05 A (d) +0.20 A (e) +0.35 A

(a) 0.13 W (b) 1.39 W (c) 2.47 W

(a) 0.05 A (b) 0.09 A (c) 0.12 A (d) 0.33 A (e) 0.47 A

(a) V_{A} - V_{B} = 10 - 10 I_{1} - 5 I_{2} (b) V_{A} - V_{B} = 10 + 10 I_{1} + 5 I_{2} (c) V_{A} - V_{B} = -6 + 50 I_{1} + 15 I_{2} (d) V_{A} - V_{B} = 6 + 50 I_{1} - 15 I_{2} (e) V_{A} - V_{B} = 6 - 50 I_{1} + 15 I_{2}

Which one of the plots at right best represents the induced current in the loop (I_{loop}) as a function of its position as it travels from the left through these three regions. Note: A positive I_{loop} means that current flows counter-clockwise.

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

Consider the two cases shown below. In each case a conductor carries the same total current I = 2 amps into the page, and in each case the current is uniformly distributed over the cross-section of the conductor.

In Case 1 the conductor is a cylindrical shell of outer radius R_{0} = 10 cm and inner radius R_{1} = 7.5 cm. In Case 2 the conductor is a solid cylinder having the same outer radius R_{0} = 10 cm.

Compare B_{1}(a), the magnitude of the magnetic field at point a (r = 5 cm) in Case 1, to B_{2}(a), the magnitude of the magnetic field at point a (r = 5 cm) in Case 2.

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

(a) -2.67 × 10^{-6} T (b) -1.33 × 10^{-6} T (c) 0 T (d) 1.33 × 10^{-6} T (e) 2.67 × 10^{-6} T

Which one of the statements at right best describes the integral of B^{.}dL along just the left most segment of the path (i.e. b → c)?

(a) (b) (c)

An infinite solid cylindrical conductor of radius a = 3 cm centered on the z-axis carries a current I_{1} = 1 A. The current is uniformly distributed over its cross section and is directed out of the page (positive z-direction). A coaxial infinite, thin cylindrical conducting shell of radius b = 8 cm carries a current I_{2} = 4 A, into the page (negative-z direction).

What is the magnitude of the B field inside the inner cylinder at a radius of 2.0 cm from the central axis?

(a) 0 (b) 1.79 × 10^{-6} T (c) 2.77 × 10^{-6} T (d) 3.58 × 10^{-6} T (e) 4.44 × 10^{-6} T

(a) The diamagnetic material is repelled by the magnet. (b) The diamagnetic material is not attracted or repelled by the magnet. Nothing happens. (c) The diamagnetic material is attracted to the magnet.

(a) The paramagnetic material is repelled by the magnet. (b) The paramagnetic material is not attracted or repelled by the magnet. Nothing happens. (c) The paramagnetic material is attracted to the magnet.

A negatively charged particle (q < 0) enters a region with uniform magnetic field B = B_{o}z. (The region with the field is shaded.) The particle has initial velocity v = v_{o}y along the y axis as shown at right.

The particle bends around in a semicircle and exits the field region a distance L from the origin. Does it exit at x = -L or at x = +L ?

(a) x = +L (b) x = -L

(a) 2 v_{o} / |q| B_{o} L (b) B_{o} L / 2 |q| v_{o} (c) |q| L / B_{o} v_{o} (d) |q| B_{o} L / 2 v_{o} (e) |q| B_{o} / 2 L v_{o}

(a) each wire experiences an attractive force, directed towards the other wire. (b) each wire experiences no net force. (c) each wire experiences a repulsive force, directed away from the other wire.