A very small circular loop of area $5 \times 10^{- 4} m^{2}$ ,resistance $2 Ω$ and negligible inductance is initially coplanar and concentric with a much larger fixed circular loop of radius 0.1m. A constant current of 1 ampere is passed in larger loop and smaller loop is rotated with a angular velocity '' $ω r a d / s$ about its diameter. The induced emf is ___ $\times 10^{- 9} V$

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$\frac{π ω}{8} \cos ω t$

$π ω^{2} \sin ω t$

$π ω \sin ω t$

$\frac{π ω}{2} \sin ω t$

answer is D.

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Detailed Solution

Induced emF in smaller loop

$e = B A N ω \sin ω t$

$e = \frac{μ_{0} i}{2 r} A ω \sin ω t$ B=magnetic induction at the centre of larger loop

$e = \frac{4 π \times 10^{- 7} \times 1 \times 5 \times 10^{- 4} \times ω \sin ω t}{2 \times (0.1)}$ $B = \frac{μ_{0} i}{2 r}$

$e = π ω \sin ω t$

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