Physics 202 MWF 10:20 Spring 1998 (Ford)

Exam III Chapts. 31-34 in SZY College Physics 7e

Show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.

(18 pts) 1. There is a uniform magnetic field B in a cylindrical region of radius a = 0.40 m. B is directed into the plane of the paper, has an initial value of 2.0 T, and is increasing in magnitude at a uniform rate of +0.05 T/s. A conducting metal ring with resistance 5.0 and radius r = 0.90 m encircles the field region, with the center of the ring at the center of the field region.

a) While the magnetic field is increasing in magnitude, what is the magnitude of the current induced in the metal ring?

Ans. ___0.0050 A___

b) Is the induced current in the ring in the counterclockwise or clockwise direction?

Ans. ___counterclockwise____


(18 pts) 2. In the sketch the rod makes contact with metal rails that are 0.20 m apart. The resistance of the conducting loop is 5.0 and may be considered to be constant. The rails are in a uniform magnetic field B that is perpendicular to the plane of the figure. If the rod is pulled to the right at a speed of 1.5 m/s, a current I = 0.04 A is induced. The induced current passes through the resistor R in the direction a to b.

a) What are the magnitude and direction (into paper or out of paper) of B?

Ans. B = ___0.667 T___

direction ___into paper___

b) What magnitude of external force F_ext is required to move the rod to the right at a constant speed of 1.5 m/s? (The magnetic field B has the same value as calculated in part (a).)

Ans. ___0.00534 N____

(20 pts) 3. Two long, straight, parallel wires carry currents I₁ and I₂ as shown in the sketch. The separation between the wires is 0.6 m. An electron (charge q = -1.60 × 10^-19 C) is moving near the wires. The electron has a constant speed of v = 4.0 × 10⁴ m/s. At the instant when the electron is moving to the right and is 0.3 m below the lower wire, what are the magnitude and direction of the resultant force that the currents in the two wires exert on the electron? (Show the direction of the force on the diagram.)

Ans. F = ___1.56 × 10^-20 N____

direction ___toward top of page____

(22 pts) 4. Consider the circuit shown in the sketch. Initially, there are no currents anywhere in the circuit.

a) The switch S is closed at time t = 0. Just after the switch is closed, what is the current i₁ through R₁, the current i₂ through R₂, and what is the voltage v_ab across the inductor?

Ans. i₁ ___2 A____

i₂ ____2 A___

v_ab ___40 V___

b) After switch S has been closed a long time, what is the current i₁ through R₁, the current i₂ through R₂, and what is the voltage v_ab across the inductor?

Ans. i₁ ____6 A____

i₂ ___0____

v_ab ___0___

c) After switch S has been closed a long time it is opened again. Just after the switch is opened again, what is the current i₁ through R₁, the current i₂ through R₂, and what is the voltage v_ab across the inductor?

Ans. i₁ ___0___

i₂ ___6 A___

v_ab ___-120 V__


(22 pts) 5. An ac series circuit consists of a source with voltage amplitude V = 120 V and angular frequency 50 rad/s, a resistor with resistance R = 400 , an inductor with inductance L =9.0 H, and a capacitor with capacitance C.

a) For what value of C will the current amplitude I be a maximum?

Ans. ___4.44 × 10^-5 F____________

b) When C has the value calculated in part (a), what is the voltage amplitude across the inductor?

Ans. ___135 V___

c) When C has the value calculated in part (a), what is the phase angle of the source voltage with respect to the current?

Ans. ___0___

d) C has the value calculated in part (a). Voltmeters V₁, V₂, and V₃, calibrated to read the rms voltage, are connected as shown below. The voltmeters each have infinite resistance so no current flows through them. What is the reading of each voltmeter?

Ans. V₁ ___84.9 V____

V₂ ___0___

V₃ ___84.9 V____