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 amont of charge which passes through any point of the loop during rotation is:

Options

A. (a) `(mu_(0)Ia)/(2pir)1n 2`
B. (b) `(mu_(0)Ia)/(pir)1n 2`
C. ( c) `(mu_(0)Ia^(2))/(2pir)`
D. (d) cannot be found because time of roattion is not given.

Answer

B

Explanation

(b) Initial flux: `phi_(i) = -int_(a)^(2a)(mu_(0)Ia)/(2pi)(dx)/(x) = -(mu_(0)Ia)/(2pi)1n 2`
Fi nal flux: `phi_(f) = -(mu_(0)Ia)/(pi r)1n 2`
Charge flown: `q = (Deltaphi)/(r ) = (phi_(f) - phi_(i))/(r ) = (mu_(0)Ia)/(pi r)1n 2`