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Question

A wire in the form of a circular loop of radius r lies with its plane normal to a magnetic field B. If the wire is pulled to take a square shape in the same plane in time t, the emf induced in the loop is given by
 


A
πBr2t(1π10)
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B
πBr2t(1π8) 
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C
πBr2t(1π6) 
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D
πBr2t(1π4) 
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Solution

The correct option is D πBr2t(1π4) 
Induced emf (e)=magnetic field×change in areatime
=BΔAt
Since the circumference of the circular loop =2πr.
the side of the square loop l=2πr4=πr2. Therefore,
ΔA=πr2(πr2)2=πr2(1π4)
e=B(πr2)t(1π4)
Hence, the correct choice is (d).

Physics

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