Question

A circuit consists of a circular of a loop of radius $R$ kept in the plane of paper and an infinitely long current carrying wire kept perpendicular to the plane of paper and passing through the centre of loop. The mutual inductance of wire and loop will be :

• A. $\frac{{\mu }_0\pi R}{2}$
• B. $0$
• C. ${\mu }_0\pi R^2$
• D. $\frac{{\mu }_0\pi R^2}{2}$

Answer 1

The correct option is B $0$

If currents in passed through the straight wire, magnetic lines are circular and tangential to the loop. So, no flux is linked with the loop.
$\varphi =\overrightarrow{B}.\overrightarrow{A}$
if $B$ and $A$ are perpendicular, their dot product is zero
Hence no EMF induced, and no mutual inductance.