Electromagnetic Induction

JEE Main level, single correct, medium

57 of 153

Question 57 of 153

A small circular loop of wire of radius aa is located at the centre of a much larger circular wire loop of radius bb. The two loops are in the same plane. The outer loop of radius bb carries an alternating current I=I0cos⁡⁡(ωt).I={I}_{0}\cos ⁡\left(\omega t\right). The emf induced in the smaller inner loop is nearly:

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Answer: (D) πμ0I02.a2bωsin⁡⁡(ωt)\dfrac{\pi {\mu }_{0}{I}_{0}}{2}.\dfrac{{a}^{2}}{b}\omega \sin ⁡\left(\omega t\right)

Induced emf,
ϵ=MdIdt,\epsilon =\dfrac{MdI}{dt},
Current is given as, I=I0cosωtI={I}_{0}cos\omega t

M=μ0πa22b,ϵ=−Mddt(I0cos⁡ωt)M=\dfrac{{\mu }_{0}\pi {a}^{2}}{2b},\epsilon =-M\dfrac{d}{dt}({I}_{0}\cos \omega t)

c=MωI0sin⁡(ωt)c=M\omega {I}_{0}\sin \left(\omega t\right)

=μ0πa22bωI0sin⁡⁡ωt=\dfrac{{\mu }_{0}\pi {a}^{2}}{2b}\omega {I}_{0}\sin ⁡\omega t

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