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. `(mu_0Ia)/(2piR)ln((2a+b)/b)`
B. `(mu_0Ia)/(2piR)ln(b/(b^2-a^2))`
C. `(mu_0Ia)/(2piR)ln((a+2b)/b)`
D. Noneof these

Answer

D

Explanation

`phi_i=int_b^(b+a)mu_0/(2pi) i/x (adx) =(mu_0ia)/(2pi) ln ((b+a)/b)`

Similarly, `phi_f=(mu_0ia)/(2pi) ln ((b-a)/b)`
`/_\phi=|Q_i-Q_f|=(mu_0ia)/(2pi) ln ((b+a)/(b-a))`
`/_\q=(/_\phi)/R=(mu_0ia)/(2piR) ln ((b+a)/(b-a))`