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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.

μ₀I4Rωπr²sinωt

μ₀I4Rωr²sinωt

μ₀I2Rωr²sinωt

μ₀I2Rωπr²sinωt

Solution:

Φ=∫∫B.dA=BAcosωt=πr²Bcosωt
ε=−dΦ/dt=−d/dt(πr²Bcosωt)=πr²Bsinωt(ω)=μ₀I2Rπωr²sinωt (∴B=μ₀I2R)