A 200-loop coil of cross sectional area 8.5 cm2 lies in the plane of the page. A

Question

A 200-loop coil of cross sectional area 8.5 cm2 lies in the plane of the page. An external magnetic field of 0.060 T is directed out of the plane of the page. The external field decreases to 0.020 T in 12 milliseconds.

(a) What is the magnitude of the change in the external magnetic flux enclosed by the coil?

(b) What is the magnitude of the average voltage induced in the coil as the external flux is changing?

(c) If the coil has a resistance of 4.0 ohms, what is the magnitude of the average current in the coil?

Explanation / Answer

N =200 loop, A =8.5 cm2, B1 =0.06 T, B2 = 0.02 T , t =12 ms

(a) Magnetic flux phi = NAB Change in magnetic flux phi2 -phi1 = NA[B2 -B1]

Change in magnetic flux = (200*8.5x10-4)[0.02-0.06]

Change in magnetic flux = -6.8 x10-3 T.m2

(b) From faradays law e = -dphi/dt e = NA(B1-B2)/t

= (6.8x10-3)/(12x10-3)

induced average voltage e = 0.567 V

(c) R =4 ohm From Ohms law e =iR induced average current i =e/R = 0.567/4 i = 0.142 A

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