An aluminum ring of radius r_1 = 5.00 cm and a resistance of 2.65 x 10^-4 ohm is

Question

An aluminum ring of radius r_1 = 5.00 cm and a resistance of 2.65 x 10^-4 ohm is placed around one end of a long air-core solenoid with 970 turns per meter and radius r_2 = 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 rate of 270 A/s. What is the induced current in the ring A At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring

Explanation / Answer

a) Iring = E/R
= [1/2[4*pi*10^-7*970*270*pi*(0.03)^2]]/[2.65*10^-4]
= 1.75 A, counterclockwise as viewed from the left hand

b)
Bring = u0*I / 2r
= [4*pi*10^-7*1.755]/[2*0.05]
= 22.05 uT

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