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Question

The induced emf in the smaller loop is
224501_7319c27b45f541fc8ad20c58b557e466.png

A
μ0πiR2r2x4v
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B
μ0πiR2r22x4v
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C
32μ0πiR2r2x4v
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D
μ0πiR2r23x4v
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E
none
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Solution

The correct option is C 32μ0πiR2r2x4v
As x>>R, in the region of smaller loop, the magnetic field produced by larger loop may be taken as uniform.
B=μoR2i2x3
and magnetic flux ϕ=BAcos0o=(μoR2i2x3)(πr2)
ϕ=μoR2iπr22x3
EMF induced e=dϕdt=μoR2iπr22ddt(1x3)=3μoR2iπr22x4dxdt
e=3μoR2iπr22x4v

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