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Question

The magnetic field in a region is given by B=B0(xa)^k. A sqaure loop of side d is placed with its edges 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
B0vod22a
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B
B0vod2a
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C
B0vod2a
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D
B0v20d2a
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Solution

The correct option is B B0vod2a

Emf in the moving conductor is given as:ε=v×Bl Since v×B is along the length of the conductor of the loop for two arms, emf induced in these arms willl be, ε=vBl.
For other two arms it is perpendicular to the length, so emf in those arms will be zero.

Let assume after some time, loop has moved a distance of x.
ε1=v0B0(x+d)ad
ε2=v0B0xad
εnet=ε1ε2=B0v0d2a

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