Physics 202 Exam 1 (Thursday, September 24) Fall 2014 (Saslow) Name (printed) Lab Section(+2 pts) Name (signed as on ID) Show all work. Partial credit will be given, if earned. Write your answers in the blanks provided. Include the correct plus or minus sign and the correct units. Total points wiil be scaled to 100. 1. (5 pts) Conducting globes A and B, on insulating bases, initially are neutral. An insulating charged rod with Q rod = 5 units of charge is brought near A, without contact or sparking. Next, holding B by its base, B is made to contact A and then is withdrawn. Finally, the charged rod is removed. Let Q A = 6 units of charge and Q B = +4 units of charge. These Q A and Q B do not violate which physics principle? a. Opposites attract and likes repel. b. Charge is conserved. c. The amount of polarization charge cannot exceed the amount that produced it. d. They violate all of the above. e. None of a-d. 2. (10 pts) For the benefit of Bart Simpson s sixth grade teacher, concisely explain the physics of the amber effect (between a charged and a neutral object) and why it is attractive. Use the figure. 3. Consider a conductor with a cavity containing an unknown charge. The conductor is in equilibrium. The total charge on the conductor itself is +4 units. If we associate 4 field lines with each unit of charge, then when viewed from afar there is a net of 12 field lines pointing into the conductor, which is in equilibrium. a. (4 pts) How much charge is within the cavity? Answer: b. (2 pts) How much charge is on the inner surface of the conductor? Answer: c. (2 pts) On the outer surface? Answer: d. (2 pts) In the bulk? Answer: 1
4. An electron in vacuum starts from rest at A, and accelerates leftward in a slightly non-uniform electric field to B. The potential changes by 5 volts when the electron moves by 4 cm. a. (3 pts) What is the direction of E? Answer: b. (3 pts) Is the potential higher or lower at B? Answer: c. (3 pts) Estimate E. Answer: d. (6 pts) How fast is the electron moving at B? Answer: 5. A quarter and a penny each sits on its own insulator. The quarter has charge 12.1 nc (n=nano=10 9 ), and the penny has an unknown charge. They are now connected by a thin insulated wire, which is then removed. a. (5 pts) The quarter now has a charge of 4.8 nc, and the penny now has a charge 3.7 nc. What was the initial charge on the penny? Answer: b. (5 pts) The voltage of the quarter is found to be 7.8V relative to a steel car bumper, and the voltage of the penny is found to be 4.2 relative to a copper door handle. What is V bumper V door? Answer: 6. Consider three capacitors. C 1 = 16 µf (micro=µ = 10 6 ) and C 2 = 14 µf are in series, and C 3 = 10 µf is in parallel with them. V c = 6 V and V b = 9 V. a. (12 pts) Find the charges Q 1, Q 2, Q 3. Answers: b. (6 pts) Find the voltage differences V 1, V 2, V 3. Answers: c. (2 pts) Find V a. Answer: 2
7. (5 pts) A 60 cm long rod with radius 3 mm carries 3 A when a voltage difference of 1.5 V (high voltage to left) is placed across its ends. The resistivity is approximately a. 2.6 10 3 Ω-m. b. 2.6 10 3 Ω/m. c. 2.4 10 5 Ω-m. d. 2.4 10 9 Ω-m. e. None of the above answers.. 8. (5 pts) Consider the equation R = V I, where electrical leads at a voltage difference V are applied at points A and B of an object, and the current I passing through the circuit is measured. Indicate the statement that is false. Choose the most appropriate answer. a. It is always true because it defines R when V and I are measured. b. There are circumstances where R = V I is not true. c. R is independent of V when Ohm s Law is true. d. In R, current passes from high V to low V when Ohm s Law is true. e. For a diode, R depends on V. 9. (5 pts) Explain why current flows through an object, and voltage does not flow across an object, but rather electrical leads at a voltage difference are placed across an object. 10. A voltaic cell has internal resistance r = 0.15 Ω and open circuit voltages across the left and right electrodes of 0.8 V and 2.6 V, for a net emf of E = 1.8 V. It is in series with a resistor R = 0.45 Ω. Let V d = 0.2 V. The connecting wires have zero resistance. a. (12 pts) Find the current, the voltage drops across the resistances, and the voltages at a, b, and c. (Hint: start from point d. A check is that V c should be the same going both and.) Answers: I =, V r =, V R =, V a =, V b =, V c = b. (3 pts) If the voltaic cell discharges in 20 minutes, find its initial charge. Answer: Q = 3
11. (30 pts) A point charge Q 1 = 2.4 10 9 C is on the positive y-axis at r 1 =4 cm from the origin. A point charge Q 2 = 1.8 10 9 C at 30 to the positive x-axis, at r 2 = 6 cm from the origin. A charge Q = 5.0 10 9 C is placed at the origin. Q 1 and Q 2 act on Q with forces F 1 and F 2. a. Find F 1 and F 2. b. On the figure, draw F 1 and F 2 with their tails on Q, and in relative proportion. c. Find F x, the x-component of the total force F on Q. d. Find F y, the y-component of F. e. Find the angle F makes with respect to the x-axis; on the figure sketch the direction of F. f. Find F. g. Find E at Q due to Q 1 and Q 2. 4
12. The circuit in the sketch consists of a battery with internal resistance r, a resistor R, and a switch. An ideal voltmeter (meaning it has such a large resistance that it draws negligible current from the rest of the circuit) V is connected in parallel to the terminals a and b of the battery. When the switch is open the voltmeter reads 3.6 V. When the switch is closed the voltmeter reads 1.8 V, and an ideal ammeter A (meaning it has such a small resistance that it hardly changes the electrical properties of the circuit) placed into the circuit) reads 0.8 A. a. (5 pts) Find the emf E of the battery. Answer: b. (5 pts) Find the internal resistance r of the battery. Answer: c. (5 pts) Find the value of R. Answer: 13. The circuit below is appropriate to jump-starting an automobile with bad battery #1 and good battery #2. Take r 1 = 4.0 Ω, r 2 = 0.01 Ω, R = 0.01 Ω. Let I 2 = 600 A, and I R = 604 A. a. (5 pts) Find I 1 through the bad battery. Answer: b. (5 pts) Find the emf E 2 of the good battery. Answer: c. (5 pts) Find the emf E 1 of the bad battery. Answer: 5