Assignment #6 PHYS 205/1-53 Electricity & Magnetism Summer 2014

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Assignment #6 - Faraday's Law, Inductance & AC circuits

Chapter 31

31-13. A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in Figure P31.13. (a) Determine the magnetic flux through the loop due to the current I. (b) Suppose the current is changing with the time according to ,I a b t= + where a and b are constants. Determine the emf that is induced in the loop if b =10.0 A/s, h = 1.0 cm, w = 10.0 cm, and L = 1.00 m. (c) What is the direction of the induced current in the rectangle?

31-15. A square, single-turn wire loop = 1.0 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3.0 cm as shown in the end view of Figure P31.15. The solenoid is 20.0cm long and wound with 100 turns of wire. (a) If the current in the solenoid is 3.0A, what is the magnetic flux through the square loop? (b) If the current in the solenoid is reduced to zero in 3.0 s, what is the magnitude of the (time) average induced emf in the square loop?

31-20. A piece of insulated wire is shaped into a figure eight as shown in Figure P31.20. For simplicity, model the two halves of the figure eight as circles. The radius of the upper circle is 5.0 cm and that of the lower circle is 9.0 cm. The wire has a uniform resistance per unit length of 3.0 /m. A uniform magnetic field is applied perpendicular to the plane of the two circles, in the direction shown. The magnetic field is increasing at a constant rate of 2.0 T/s. Find (a) the magnitude and (b) the direction of the induced current in the wire.

31-26. Consider the arrangement shown in Figure P31.26. Assume that R = 6.00 , = 1.20 m, and a uniform 2.5-T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.500 A in the resistor.

Chapter 32

32- 4. A solenoid of radius 2.5 cm has 400 turns and a length of 20.0 cm. Find (a) its inductance and (b) the rate at which current must change through it to produce an emf of 75.0 mV.

32-57. In Figure P32.56, let R= 7.60 , L = 2.20 mH, and C = 1.80 F. (a) Calculate the frequency of the damped oscillation of the circuit when the switch is thrown to position b. (b) What is the critical resistance for damped oscillations?

Chapter 33

33-71. In Figure P33.71, find the rms current delivered by the 45.0 V (rms) power supply when (a) the frequency is very large and (b) the frequency is very small.

33-75. A series RLC circuit consists of an 8.00- resistor, a 5.00-F capacitor, and a 50.0-mH inductor. A variable-frequency source applies an emf of 400 V (rms) across the combination. Assuming the frequency is equal to one-half the resonance frequency, determine the power delivered to the circuit.

R

Figure P31.26

FapplBin

l

l

r

Figure P31.15

Figure P31.13

w

L

h

I

o oo o

Figure P33.71

45.0 V(rms)100 3.0 mH

200 200 F

Figure P31.20

L

R

a S

b

CE +

Figure P32.56