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In figure, a square loop PQRS of side a and resistance r is placed near an infinitely long wire carrying a constant current I. The sides PQ and RS are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by 1800 about an axis parallel to the long wire and passing through the midpoints of the sides QR and PS. The total amount of charge which passes through any point of the loop during rotation is

a
μ0Ia2πrIn 2
b
μ0IaπrIn 2
c
μ0Ia22πr
d
Cannot be found because time of rotation is not given.

detailed solution

Correct option is B

Initial flux:ϕ1=-∫a2aμ0Ia2πdxx=-μ0Ia2πIn2Final flux: ϕf=μ0Ia2π In 2charge flown: q=∆ϕr=ϕf-ϕir=μ0Iaπr In 2

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