First slide

Faraday's law of Electromagnetic induction

Question

The radius of a coil decreases steadily at the rate of 10^-2 m/s. A constant and uniform magnetic field of induction 10^-3 Wb/m² acts perpendicular to the plane of the coil. The radius of the coil when the induced emf in the coil is 1μV is :

Moderate

A

$\frac{2}{π} cm$
B

$\frac{3}{π} cm$
C

$\frac{4}{π} cm$
D

$\frac{5}{π} cm$

Solution

$e = \frac{dϕ}{dt} = \frac{d}{dt} ({πr}^{2} B) = 2 πrB \frac{dr}{dt} \Rightarrow r = \frac{e}{(2 πB \frac{dr}{dt})} \Rightarrow r = \frac{10^{- 6}}{2 π x 10^{- 3} x 10^{- 2}} = \frac{5}{π} cm$

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