At the centre of a fixed large circular coil of radius R , a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current

Question

At the centre of a fixed large circular coil of radius R , a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity ω about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time t of its start of rotation.

TestHub · Accepted Answer

According to Faraday's law of electromagnetic induction, e = − d t d ϕ ​ and ϕ = B A cos ω t = B π r 2 cos ω t ⇒ e = − d t d ​ ( π r 2 B cos ω t ) = π r 2 B sin ω t ( ω ) ∴ e = 2 R μ 0 ​ I ​ πω r 2 sin ω t ( ∵ B = 2 R μ 0 ​ I ​ ) ​

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