A 2.20 cm diameter ring moves from a a region with no magnetic field into a 2.00

Question

A 2.20 cm diameter ring moves from a a region with no magnetic field into a 2.00 T field (out of the page) with the ring parallel to the field. It takes 0.250 s for the ring to move into the magnetic field (4 parts).

A. Find the emf induced in the ring.

B. What is the magnitude and direction of the current induced if its resistance is 0.0100 Ohms?

C. What magnetic field is induced at the center of the ring? What is the direction of the induced magnetic field?

D. Would your answer change if the ring was stationary and the magnetic field moved? Explain.

Explanation / Answer

the induced emf in the ring is

E =N d( B A)/ dt = N A dB/ dt = 1 pi ( 2.2* 10 ^-2 m/2)^2 ( 2 T/0.250 s) = 3.04 mV

(b)

induced current

I = E/R = 3.04 mV/ 0.0100 ohms = 0.3039 A

(c)

B = uoi / 2 r = 4 pi * 10 ^-7 ( 0.3039)/ 2( 1.1 * 10 ^-2 m) = 1.73 * 10 ^-5 T

(d)

No, magnetic field does not change , by varying magnetic field induced emf changes

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