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Question

A long conducting wire AH is moved over a conducting triangular wire CDE with a constant velocity v in a uniform magnetic field B directed into the plane of the paper. Resistance per unit length of each wire ρ. Then
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A
a constant clockwise induced current will flow in the closed loop
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B
an increasing anticlockwise induced current will flow in the closed loop
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C
a decreasing anticlockwise induced current will flow in the closed loop
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D
a constant anticlockwise induced current will flow in the closed loop
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Solution

The correct option is D a constant anticlockwise induced current will flow in the closed loop
Intial flux = 12xhB

flux at time t = 12(xh(h+vt))(h+vt)B=12xh(h+vt)2B

emf=rate of change of flux= xh(h+vt)v

length of loop at time t = xh(h+vt)+2yh(h+vt)=k(h+vt) ;k=xh+2yh

resistance of loop = ρk(h+vt)

current at time t = emfresistance= independent of t.

As the flux keeps increases through the flux , by Lenz's Law, induced current will be in the anticlockwise direction. And from the above calculations, current will be constant.

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