A magnetic field is passing through a loop of wire whose area is 0.016 m 2 . The

Question

A magnetic field is passing through a loop of wire whose area is 0.016 m2. The direction of the magnetic field is parallel to the normal to the loop, and the magnitude of the field is increasing at the rate of 0.23 T/s. (a) Determine the magnitude of the emf induced in the loop. (b) Suppose the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m^2/s) should the area be changed at the instant when B = 1.4 T if the induced emf is to be zero? Use a minus sign if the area is to be shrunk.

Explanation / Answer

(A) induced emf = rate of change of magnetic flux

= d(NBA)/dt

= N A dB/dt

= 1 x 0.016 m^2 x 0.23 T/s

= 3.68 x 10^-3 Volt Or 3.68 mV

(b) e = d(BA)/dt

= B dA/dt + AdB/dt

0 = 1.4 (dA/dt) + (0.016)(0.23)

dA/dt = - 2.63 x 10^-3 m^2 / s

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