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 96. The exam period was 90 minutes; the mean was 72.1; the median was 74. Click here to see page1 page2 of the formula sheet that came with the exam.

Four infinite wires carry currents parallel to the z-axis as shown in the figure. Each wire is spaced from the z-axis by a meters. The magnitude of the current in each of the wires is equal to I_{0}. Two of the wires carry current in the positive z-direction and two of the wires carry current in the negative z-direction.

What is the magnetic field B(0) at the origin?

(Hint: Use the principle of superposition and the right hand rule to solve this. Keep track of the contribution from each wire.)

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

(a) The magnetic field everywhere stays the same. (b) The magnetic field everywhere is one half what it was before. (c) The magnetic field at the origin goes to zero.

An infinite coaxial cable consists of a solid center conductor of radius 0.01 meter, and an outer conducting cylindrical shell of radius 0.1 meter. A small section of the cable is shown in the figure. A current of 4 amperes flows to the right uniformly distributed in the center conductor and a current of 2 amperes flows to the left uniformly distributed on the outer conductor. The center of the coaxial cable is the axis of cylindrical symmetry.

What is the magnitude of the magnetic field 0.8 meter from the axis of cylindrical symmetry?

(a) 2.0 × 10^{-7} tesla (b) 5.0 × 10^{-7} tesla (c) 8.0 × 10^{-7} tesla (d) 1.0 × 10^{-6} tesla (e) 1.5 × 10^{-6} tesla

(T) True (F) False

Between time t = 0 and t = τ the magnetic field in the region of space pertaining to this problem is given by B(t) = B_{0}(1-t/τ)z, where B_{0} is a positive number. At earlier times the field is constant and is given by B(t) = B_{0}z and at later times the field is zero. This means that the magnetic field at time t = 0 points in the positive z-direction and has a magnitude of B_{0} and then it linearly decreases in magnitude reaching zero at time t = τ. This is shown on the graph below. A conducting loop of area A that incorporates a resistor with a resistance R_{0} lies in the x-y plane as shown in the adjacent figure.

Which one of these statements regarding the current in the loop during the time interval between t = 0 and t = τ is true?

(a) Since there is no battery, there is no current. (b) There is a current that flows counter-clockwise as viewed from above. (c) There is a current that flows clockwise as viewed from above.

(a) ε = 2τR_{0} / B_{0} (b) ε = AB_{0} / τ (c) ε = AτB_{0} (d) ε = τB_{0} / R_{0} (e) ε = AR_{0}B_{0} / 2τ

Two batteries are arranged in a circuit with two resistors as shown in the figure. The resistance of each resistor is not given, but the indicated currents are observed to flow through the two resistors. (Hint: Redraw the circuit to see explicitly what circuit elements are in series and which are in parallel. Pay attention to the polarity of the batteries in the figure.)

Which battery supplies the most power to the resistors?

(a) the 20 V battery (b) the 30 V battery

(a) 12.5 Ω (b) 10 Ω (c) 5 Ω (d) 4 Ω (e) 2 Ω

A circuit consists of a capacitor, two 10 Ω resistors, and a 100 V battery connected as shown in the figure. The switch is closed (connected) at time t = 0. Assume that the capacitor is uncharged before the switch is closed.

It is observed that the charge stored on the capacitor as a function of time while it charging is given by

Find the capacitance C of the capacitor

(a) 1.0 × 10^{-8} farads (b) 5.0 × 10^{-8} farads (c) 1.0 × 10^{-7} farads (d) 2.0 × 10^{-7} farads (e) 1.0 × 10^{-6} farads

(a) At t = 0 the same current flows through the two resistors. (b) At t = ∞ the same current flows through the two resistors. (c) At t = 0 twice the current flows through one resistor compared to the other.

A circuit is constructed out of a 0.01 F capacitor, four resistors, and a 30 V battery connected as shown in the figure. The switch is closed (connected) at time t = 0. Assume that the capacitor is uncharged before the switch is connected.

At t = 0 the current flowing though the battery is:

(a) 2.06 A (b) 1.08 A (c) 2.54 A

(a) 1.125 J (b) 1.000 J (c) 0.750 J (d) 0.125 J (e) 0.050 J

(a) The stored energy in the capacitor with 20 Ω resistors is larger than the stored energy with 15 Ω resistors. (b) The stored energy in the capacitor with 20 Ω resistors is smaller than the stored energy with 15 Ω resistors. (c) The stored energy in the capacitor with 20 Ω resistors is equal to the stored energy with 15 Ω resistors.

A neutral, conducting rod of length L = 0.4 m is moving with constant speed v = 2 m/s in the positive x direction in the presence of a magnetic field B = 0.35 T directed into the page as shown.

The bottom end of the rod has

(a) excess + charge. (b) excess - charge.

(a) 0.7 V/m (b) 0.28 V/m (c) 1.75 V/m

A single circular loop of wire of radius R = 0.24 m carries current I = 0.4 A, and is oriented as shown in the diagram. A constant magnetic field points along the negative y-direction having magnitude B = 0.7 T. To begin with, the loop is fixed in space.

In the diagram at the right, the two arrows labeled "a)" and "b)" denote two possible directions for the magnetic moment of the loop. Which is actually the correct direction?

(a) Orientation "a)" is correct for the magnetic moment. (b) Orientation "b)" is correct for the magnetic moment.

(a) 0.025 N⋅m (b) 0.044 N⋅m (c) 0.066 N⋅m (d) 0.21 N⋅m (e) 0.37 N⋅m

(a) (b)

(a) increases. (b) decreases.

Two charged particles enter a region of constant and uniform magnetic field directed out of the page (positive z direction) through a small opening traveling along the positive y-axis. The path taken by the two particles is shown in the diagram. Both particles enter the region of magnetic field with the same speed and both have the same magnitude charge.

What type of charge are the two particles?

(a) Particle #1 is + and particle #2 is -. (b) Particle #1 is - and particle #2 is +.

(a) 0.186 m (b) 0.215 m (c) 0.372 m (d) 0.487 m (e) 0.669 m

(a) 9.6 × 10^{-16} V/m directed toward the bottom of the page (b) 6.0 × 10^{3} V/m directed toward the bottom of the page (c) 9.6 × 10^{-16} V/m directed toward the top of the page (d) 6.0 × 10^{3} V/m directed toward the top of the page (e) 9.6 × 10^{-16} V/m directed out of the page.

(a) Situation 1 (b) Situation 2 (c) Situation 3 (d) Situations 2 and 3 (e) Situations 1, 2 and 3