A toy electric generator has a 20-turn circular coil with each turn of radius 1.

Question

A toy electric generator has a 20-turn circular coil with each turn of radius 1.8 cm. The coil resides in a 1.0-T magnitude B field. It also has a lightbulb that lights if the potential difference across it is about 1 V. You start rotating the coil, which is initially perpendicular to the B field.

If the time interval for one rotation is reduced by one-fourth while the radius of the coil is reduced by one-half, how will emf change?

If the time interval for one rotation is reduced by one-fourth while the radius of the coil is reduced by one-half, how will emf change?

Einnew=1/2×Einold

Einnew=1/2×Einold

Explanation / Answer

Given, N = 20

r = 1.8 m

b = 1 T

induced emf, Einold = N*A_old*dB/dt_old

1) If the time interval for one rotation is reduced by one-fourth while the radius of the coil is reduced by one-half,

dt_new = dt_old/4

r_new = r_old/2

so, A_new = A_lod/4

so, Ein_new = N*A_new*dB/dt_new

= N*(A_old/4)*dB/(dt_old/4)

= N*A_old*dB/dt_old

= Ein_old <<<<<<<<<----------------Answer

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