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 126. The exam period was 90 minutes; the mean score was 97.4 the median was 100. 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}.

For this and the next two questions, ignore all forces but the electrostatic.

Three charges (-q, -q, +3q) are located in the xy plane as shown in the figure.

How much work W is required to bring a charge +2q from infinity to position (x,y) = (d,0) for the charge configuration in this picture?

(a) W = -4.45 J (b) W = -0.13 J (c) W = 0 J (d) W = +0.13 J (e) W = +4.45 J

(a) F_{x} = -10.8 N (b) F_{x} = -7.6 N (c) F_{x} = 0 N (d) F_{x} = +7.6 N (e) F_{x} = +10.8 N

(a) E = 0 N/C (b) E = 1.2 × 10^{6} N/C (c) E = 2.4 × 10^{6} N/C

Given is a map of equal-potential lines (see figure below). The potential is created by three charges in a plane (q_{1}, q_{2}, q_{3}). Potential values are given in volts. Note the signs (+/-).

Based on the map, what is the sign (+/-) of the charge q_{3}?

(a) - (b) 0 (c) +

(a) left (b) right (c) up (d) down (e) cannot be determined

(a) W = -4 J (b) W = -2 J (c) W = 0 J (d) W = +2 J (e) W = +4 J

(a) C_{AB} = 9.2 μF (b) C_{AB} = 22.2 μF (c) C_{AB} = 25 μF (d) C_{AB} = 50 μF (e) C_{AB} = 90 μF

(a) q, -3q (b) -q, -q (c) 0, -2q (d) 2q, -2q (e) 0, 0

The membrane of a living cell can be viewed as a parallel-plate capacitor. For a specific type of cell, the dielectric constant of the membrane is κ = 3, the width of the membrane is d = 7 nm (1 nm = 10^{-9} m) and total surface area of the membrane is A = 10^{-10} m^{2}. The potential difference across the capacitor is maintained by charged ions.

What is the capacitance C of the cell membrane?

(a) C = 1.9 × 10^{-9} F (b) C = 1.9 × 10^{-13} F (c) C = 3.8 × 10^{-13} F

(a) N = 3.2 × 10^{-14} (b) N = 2.0 × 10^{5} (c) N = 6.2 × 10^{23}

(a) U_{0} = -1.4 × 10^{-15} J (b) U_{0}= +1.4 × 10^{-15} J (c) U_{0} = 1.4 × 10^{-6} J

(a) U' = ½ U_{0} (b) U' = U_{0} (c) U' = 2U_{0}

A capacitor array is shown in this figure. Each capacitor is identical with unknown capacitance C. An unknown potential difference V_{0} is maintained by a power supply. The equivalent capacitance of the network is 6 μF.

What is the capacitance C of each of the individual capacitors?

(a) C = 2 μF (b) C = 4 μF (c) C = 6 μF (d) C = 9 μF (e) C = 12 μF

(a) V_{0} = 0.8 V (b) V_{0} = 1.2 V (c) V_{0} = 3.5 V (d) V_{0} = 7.0 V (e) V_{0} = 9.0 V

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

(a) U_{tot} = 40 mJ (b) U_{tot} = 100 mJ (c) U_{tot} = 140 mJ

In the circuit shown, the switch S has been open for a long time so that the capacitor is uncharged.

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

(a) I (0+) = 0 (b) I (0+) = V / (2R) (c) I (0+) = V / R

(a) I (∞) = 0 (b) I (∞) = V / (2R) (c) I (∞) = V / R

(a) Q (∞) = CV / 2 (b) Q (∞) = CV (c) Q (∞) = 2CV

(a) t = 13.8 μs (b) t = 27.7 μs (c) t = 55.5 μs (d) t = 88.1 μs (e) t = 113.2 μs

An isolated parallel plate capacitor contains charge Q_{0} = ±10 μC on its plates, corresponding to a potential difference of V_{0} = 10 V. The initial separation between the plates is d. Later, the distance between the plates is increased by a factor of two while the charge on each plate remains unchanged.

What is the voltage V' between the two plates after the separation becomes 2d?

(a) V' = 2.5 V (b) V' = 5 V (c) V' = 10 V (d) V' = 20 V (e) V' = 40 V

(a) [ U_{2d} / U_{d} ] > 1 (b) [ U_{2d} / U_{d} ] = 1 (c) [ U_{2d} / U_{d} ] < 1

In the circuit shown below, the battery voltage is ε, the resistors R_{1} = R_{3} = R and R_{2 } = R_{4} = 2R.

What is the equivalent resistance R_{eq} for this configuration of resistors?

(a) R_{eq} = 5 R (b) R_{eq} = R / 10 (c) R_{eq} = 3 R / 2 (d) R_{eq} = 6 R / 5 (e) R_{eq} = R

(a) P_{34} = ε^{2} / 10R (b) P_{34} = ε^{2} / R (c) P_{34} = ε^{2} / 5R (d) P_{34} = ε^{2} / 20R (e) P_{34} = ε^{2} / 3R

(a) R = 3 Ω (b) R = 1 Ω (c) R = 10 Ω (d) R = 2 Ω (e) R = 0.1 Ω

(a) V_{AB} > 0 (b) V_{AB} < 0 (c) V_{AB} = 0

What should be the resistance R so that the lamp works as designed?

(a) R = 0.12 Ω (b) R = 0.54 Ω (c) R = 2.67 Ω (d) R = 5.78 Ω (e) R = 98 Ω

Which one of the following equations is correct?

(a) ε_{1 }+ I_{1} R_{1} - ε_{2} + I_{1} R_{2} = 0 (b) I_{1} - I_{2} = I_{3} (c) -ε_{1} + I_{1} ( R_{1} + R_{2}) + I_{3} R_{3} = 0