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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 $' ω' {rads}^{- 1}$ about its diameter. The induced emf is ___ $\times 10^{- 9} V$

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π ω \sin ω t

π ω^{2} \sin ω t

\frac{π ω}{2} \sin ω t

\frac{π ω}{8} \cos ω t

answer is D.

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Detailed Solution

e = \frac{d}{dt} (BA \cos ω t) = BA ω \sin ω t

$B = \frac{μ_{0} i}{2 r}$

$e = \frac{4 π \times 10^{- 7} \times 1}{2 \times 0.1} \times 5 \times 10^{- 4} ω \sin ω t$

$e = π ω \sin ω t$

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