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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 - [JEE-Main On line-2018]
- μ₀Iω/(2R) · ωr² sin ωt
- μ₀Iω/(4R) · ωπr² sin ωt
- μ₀I/(2R) · ωπr² sin ωt
- μ₀Iω/(4R) · ωr² sin ωt
Correct answer: μ₀I/(2R) · ωπr² sin ωt
Solution
Field at the centre of the large coil is B = mu0*I/(2R). The small coil of area pi*r^2 rotating at w gives emf = B*(pi*r^2)*w*sin(wt) = mu0*I*pi*r^2*w*sin(wt)/(2R).
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