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Question

The magnetic field in a region is given by B=B0(1+xa)^k. A square loop of edge length d is placed with its edge along the x- and y-axes. The loop is moved with a constant velocity v=v0^i. The emf induced in the loop is

A
v0B0d2a
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B
v0B0d3a2
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C
v0B0d
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D
2v0B0d
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E
zero
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Solution

The correct option is E v0B0d2a
ϕ=x+dxB.dA=x+dxBo(1+xa)ddx=Bod(d+(x+d)2x22a)
By faraday's law
ϵ=dϕdt=dϕdxdxdt
=Bod2d2avo

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