An aluminum ring of radius r1 = 5.00 cm and a resistance of 3.05 10-4 ? is place

Question

An aluminum ring of radius r1 = 5.00 cm and a resistance of 3.05 10-4 ? is placed around one end of a long air-core solenoid with 900 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?
A

(b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring?
?T

Explanation / Answer

a)

emf = (1/2)(0)(900 turns / meter)(270 A / s)[(0.03m)2]

emf = 0.5*4*3.14e-7*900*270*3.14*0.03*0.03 = 0.00043126 V

I = emf/R = 0.00043126/3.05e-4 = 1.4140 1.41 A

b)

B = i/2R = 4*3.14e-7*1.4140/(2*0.05) = 17.8 T

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