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2049 Spring 2005 Quiz 6 Name: Period: Question 1 A metal ring of radius a and resistance R sits on top of a solenoid of length L. A current i passes around the N turns of the solenoid (also of radius a). The current is now increased with time. (a) At any instant, what is the magnetic field inside the solenoid (1 point)? The magnetic field is due to the solenoid and is given by Ampere’s law: B = µ0 is N . L (1) (b) What is the induced emf in the ring (Compute both its magnitude and indicate its flow relative to the current in the solenoid) (1 point)? Faraday’s Law states: dΦB N dis E =− = −µ0 . (2) dt L dt Since the current is increasing with time, the induced emf and hence current must flow counter to the direction of is . (c) What happens to the ring (1 point)? Opposite currents repel, and therefore the ring will jump off the solenoid. Question 2 (3 points) A rectangular loop of wire with length a, width b, and resistance R is placed near an infinitely long wire carrying current i, as shown below. The distance from the long wire to the center of the loop is r. Find the magnitude of the magnetic flux through the loop. a b r i Z ~·B ~ , dA ΦB = S Z a = Z r+b/2 dx 0 Z (3) dyB(y) , r+b/2 dy , r−b/2 y µ ¶ µ0 ia 2r − b = ln . 2π 2r + b = µ0 ia 2π (4) r−b/2 (5) (6)