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In the figure shown 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 180° about an axis parallel to the long wire and passing through the mid points of the side QR and PS. The total amount of charge which passes through any point of the loop during rotation is:

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Cannot be found because time of rotation not given

$\frac{μ_{0} Ia}{2 πr} In 2$

$\frac{μ_{0} {Ia}^{2}}{2 πr}$

$\frac{μ_{0} Ia}{πr} In 2$

answer is B.

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Detailed Solution

$ϕ = \frac{μ_{0} Ia}{2 π} In 2$ When loop is rotated through 180°, change in magnetic flux is $Δϕ = 2 ϕ = \frac{2 μIa}{2 π} In 2$

So, charge flown $q = \frac{Δϕ}{r} = \frac{μ_{0} Ia}{πr} In 2$

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