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Q.

Four different uniform and constant magnetic fields B→1=B0k^,B→2=2B0k^,B→3=3B0k^ and B→4=4B0k^ exist in first, second, third and fourth quadrant respectively of x-y plane as shown in figure. A square wireframe PQRS of one side I and total resistance R lying in x-y plane is moving with velocity v→=v0i^ such that its centre lies on x-axis and side PQ is parallel to x-axis. B0 and v0 are positive constants. Then the magnitude of current induced in the square loop at the instant its centre lies of origin is

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a

0

b

Blv0R

c

Blv02R

d

2Blv0R

answer is A.

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Detailed Solution

As the loop PQRS moves in positive x-direction, the flux through loop does not change. Hence induced emf and induced current through the loop is zero.
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Four different uniform and constant magnetic fields B→1=B0k^,B→2=2B0k^,B→3=3B0k^ and B→4=4B0k^ exist in first, second, third and fourth quadrant respectively of x-y plane as shown in figure. A square wireframe PQRS of one side I and total resistance R lying in x-y plane is moving with velocity v→=v0i^ such that its centre lies on x-axis and side PQ is parallel to x-axis. B0 and v0 are positive constants. Then the magnitude of current induced in the square loop at the instant its centre lies of origin is