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A magnetic field of $2 \times 10^{- 2} T$ acts at right angles to a coil of area $100 c m^{2}$ with 50 turns. If the average emf induced in the coil is $0.1 V$ when it is removed from the field in time $t .$ The value of $‘ t ’$ is

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0.1 s

0.01 s

1 s

20 s

answer is A.

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Detailed Solution

$B = 2 \times 10^{- 2} T A = 100 c m^{2} = 100 \times 10^{- 4} m^{2}$

$N = 50, e = 0.1 V$

$e = \frac{d ϕ}{d t} = \frac{(ϕ_{2} - ϕ_{1})}{t}$

Coil is removed from the field $\Rightarrow ϕ_{2} = 0$

$|e| = \frac{ϕ_{1}}{t} = \frac{B A N}{t}$

$t = \frac{B A N}{e} = \frac{2 \times 10^{- 2} \times 10^{- 2} \times 50}{0.1} = 0.1 s$

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