`AB` is an infinitely long wire placed in the plane of rectangular coil of dimension as shown in the figure. Calculate the mutual inductance of wire `AB` and coil `PQRS`

Options

A. `(mu_0b)/(2pi) ln a/b`
B. `(mu_0c)/(2pi) ln b/a`
C. `(mu_0abc)/(2pi(b-a)^2)`
D. None of these

Answer

B

Explanation

`B=mu_0/(2pi) i/ximplies dS =cdx`
`dphi=BdS =mu_0/(2pi) (iC)/x dx`
`phi=int_a^b dphi=(mu_0iC)/(2pi) ln (b/a)`
`M=phi/t=(mu_0c)/(2pi) ln (b/a)`