An aluminum ring of radius r1 and resistance R is placed around the top of a long air-core solenoid with n turns per meter and smaller radius r 2 as shown in Figure P31.7. Assume that the axial component of the field produced by the solenoid over the area of the end of the solenoid is half as strong as at the center of the solenoid. Assume that the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of ∆I/∆t.
(a) What is the induced current in the ring?
(b) At the center of the ring, what is the magnetic field produced by the induced current in the ring?
(c) What is the direction of this field?