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 119. The exam period was 90 minutes; the mean score was 91.6; the median was 93. Click here to see page1 page2 of the formula sheet that came with the exam.

Which one of the three diagrams given below shows the correct equipotential contours associated with this dipole?

(a) (b) (c)

(a) E_{A} < E_{B} (b) E_{A} = E_{B} (c) E_{A} > E_{B}

(a) xy-plane (b) yz-plane (c) zx-plane

With the battery still connected, the thick conducting slab shown at the right is placed symmetrically between the two plates. What is the effect on the capacitance C?

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

A positive point charge +Q_{0} is located at point P a distance d from a large thin sheet with uniform positive charge density σ_{o}. A cylindrical Gaussian surface encloses the +Q_{0} charge and a portion of the sheet as shown.

Let Φ_{o} represent the outward flux through the curved side wall (the barrel) of the Gaussian surface. Which one of the following relations is correct?

(a) Φ_{o} > 0 (b) Φ_{o} = 0 (c) Φ_{o} < 0

Which of the following describes how the magnitude of the net flux through the left end cap changes when the new charge is introduced?

(a) | Φ_{after} | > | Φ_{before} | (b) | Φ_{after} | = | Φ_{before} | (c) | Φ_{after} | < | Φ_{before} |

Two charged rods, each with positive net charge Q_{0}, are held in place as shown in the top view diagram below.

A small positive test charge q_{0} travels from point A to point B along the circular arc shown. The work done on the charge by the electric field is

(a) positive. (b) negative. (c) zero.

(a) | v_{A} | > | v_{B} | (b) | v_{A} | = | v_{B} | (c) | v_{A} | < | v_{B} |

Three thick conducting infinite planes are oriented perpendicular to the x axis, and placed at the positions given in the figure below. Each plane carries a net charge, as indicated in the legend.

A negatively charged object placed at x = +4 cm and released would experience a force in the positive x direction.

(T) True (F) False

(a) 1 region (b) 3 regions (c) 5 regions

(a) E_{x} = 0 (b) E_{x} = 3.39 × 10^{5} N/C (c) E_{x} = 7.58 × 10^{5} N/C (d) E_{x} = 11.5 × 10^{5} N/C (e) E_{x} = 14.6 × 10^{5} N/C

(a) σ_{L} = -6 μC/m^{2} (b) σ_{L} = -3 μC/m^{2} (c) σ_{L} = 0 (d) σ_{L} = 3 μC/m^{2} (e) σ_{L} = 6 μC/m^{2}

Consider an infinite line with charge density λ_{0} = +3 μC/m, shown in the center of the figure below. Concentric with the line is a hollow thick-walled cylinder (shaded), made of conducting material. The hollow cylinder carries a charge per unit length of λ = -3 μC/m. Finally, a thin nonconducting cylindrical shell is concentric with the other two objects, and carries a charge per unit length of λ_{c} = +6 μC/m. The dimensions of the objects are shown in the figure; all three have infinite length.

What is the surface charge density σ_{b} on the outer surface of the thick conducting shell?

(a) σ_{b} > 0 (b) σ_{b} = 0 (c) σ_{b} < 0

(a) E = 0.54 × 10^{6} N/C (b) E = 1.23 × 10^{6} N/C (c) E = 3.15 × 10^{6} N/C (d) E = 5.57 × 10^{6} N/C (e) E = 7.14 × 10^{6} N/C

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

Three massive charged balls are positioned as shown in the figure below. A frictionless rod running along the x axis constrains the motion of Ball #3 to slide along this axis. Ball #1 and Ball #2 are fixed on the y axis at + 4 cm and -4 cm, respectively. Ball #3 is initially located at x = 8 cm and is held fixed.

How much total energy is required to assemble these Balls into their initial positions assuming they all start off infinitely far away?

(a) U_{total} = -3.11 J (b) U_{total} = -1.59 J (c) U_{total} = 0 (d) U_{total} = 2.34 J (e) U_{total} = 8.94 J

(a) eventually come to rest at the origin. (b) oscillate back and forth along the x axis about the origin. (c) fly off to negative infinity along the x axis.

(a) V(0) = 0 (b) V(0) = 0.94 × 10^{5} J/C (c) V(0) = 2.15 × 10^{5} J/C (d) V(0) = 5.63 × 10^{5} J/C (e) V(0) = 7.42 × 10^{5} J/C

(a) F_{x} = -11.5 N (b) F_{x} = -18.1 N (c) F_{x} = -24.4 N (d) F_{x} = -30.7 N (e) F_{x} = -39.5 N

A conducting sphere of radius a = 20 cm carries a charge of +6 μC. Concentric with this sphere is a non-conducting spherical shell with an inner radius of b = 70 cm and an outer radius of c = 80 cm. This shell carries a charge of -6 μC, distributed uniformly throughout the material of the shell.

As one moves from a position very far from these two objects to a point just outside the nonconducting shell, the electric potential

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

(a) W_{cb} > 0 (b) W_{cb} = 0 (c) W_{cb} < 0

(a) | ΔV_{ab} | = 7.1 × 10^{5} V (b) | ΔV_{ab} | = 5.9 × 10^{5} V (c) | ΔV_{ab} | = 3.3 × 10^{5} V (d) | ΔV_{ab} | = 1.9 × 10^{5} V (e) | ΔV_{ab} | = 0

(a) F = 0 (b) F = 2.31 N (c) F = 3.58 N (d) F = 5.06 N (e) F = 7.45 N

Three capacitors are connected as shown in the figure below. The gaps between the plates of all three capacitors are filled with air (κ = 1.0), giving the capacitance values listed in the figure. A constant potential difference of 6 V is maintained between points A and B on the circuit.

What is the magnitude of the charge Q_{2} on each of the plates of capacitor C_{2}?

(a) Q_{2} = 24 μC (b) Q_{2} = 12 μC (c) Q_{2} = 6 μC (d) Q_{2} = 3 μC (e) Q_{2} = 2 μC

(a) U_{tot} = 22.2 μJ (b) U_{tot} = 33.7 μJ (c) U_{tot} = 44.5 μJ (d) U_{tot} = 55.3 μJ (e) U_{tot} = 66.9 μJ

(a) V_{3} = 1.78 V (b) V_{3} = 2.60 V (c) V_{3} = 3.43 V (d) V_{3} = 4.04 V (e) V_{3} = 4.85 V

(a) | ΔU_{2} | = 76.4 μJ (b) | ΔU_{2} | = 158 μJ (c) | ΔU_{2} | = 267 μJ (d) | ΔU_{2} | = 378 μJ (e) | ΔU_{2} | = 480 μJ