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Q.

A straight conducting rod PQ is executing SHM in xy-plane from x=-d to x=+d. Its mean position is x=0 and its length is along y-axis. There exists a uniform magnetic field B from x=-d to x=0 pointing inward normal to the paper and from x=0 to x=+d there exists another uniform magnetic field of same magnitude B but pointing outward normal to the plane of the paper. At the instant t=0, the rod is at x=0 and moving to the right. The induced emf ε across the rod PQ vs time t graph will be

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a

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b

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c

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d

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answer is B.

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Detailed Solution

At mean position, velocity is maximum. Hence, motional emf Bvl is also maximum. v oscillates simple harmonically. Hence, motional emf will also move simple harmonically. Further, polarity of induced emf will keep on changing.

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