An 800-turn coil of effective area $0.05$ m$^2$ is kept perpendicul...

Question

An 800-turn coil of effective area $0.05$ m$^2$ is kept perpendicular to a magnetic field $5 	imes 10^{-5}$ T. When the plane of the coil is rotated by 90° around any of its coplanar axes in 0.1 s, find the emf induced in the coil.

Accepted Answer

Initial flux (coil perpendicular to $B$, i.e., normal parallel to $B$):

$$\Phi_i = NBA = 800 \times 5 \times 10^{-5} \times 0.05 = 2 \times 10^{-3} \text{ Wb}$$

Final flux (after rotating 90°, normal perpendicular to $B$):

$$\Phi_f = NBA\cos 90° = 0$$

Induced emf:

$$\varepsilon = -\frac{\Delta\Phi}{\Delta t} = -\frac{0 - 2 \times 10^{-3}}{0.1} = \frac{2 \times 10^{-3}}{0.1} = 0.02 \text{ V}$$

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