A square loop of side as and a straight long wire are placed in the same plane as shown in figure. The loop has a resistance `R` and inductance `L`. The frame is turned through `180^@` about the axis `OO^'`. What is the electric charge that flows through the loop?

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`