Question

An aluminum ring of radius r1 = 5.00 cm and a resistance of 4.35 X 104 12 is placed around one end of a long air-core solenoid with 1 050 turns per meter and radius r2 = 3.00 cm as shown in the figure below. Assume the axial component of the field produced by the solenoid is one-half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring? (b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring? UT (c) At the center of the ring, what is the direction of the magnetic field produced by the induced current in the ring? O to the left to the right O upward downward

Answer 1

A)

Current, I = E/R

E = 0.5 u0 n pi r2^2 (dI/dt)

E = 0.5 x 4 pi x 10^-7 x 1050 x pi x 0.03^2 x (270) = 5.04 x 10^-4 V

I = 5.04 x 10^-4/0.000435 = 1.16 A

B)

B = u0 I/2 r1

B = (4 pi x 10^-7 x 1.16)/(2 x 0.05) = 14.55 uT

C)

Left

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