Question

A long straight wire carrying current $i$ is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

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

Answer 1

The correct option is D Zero


The magnetic field produced by the long wire is in the same plane as that of the circular wire. Therefore, the angle between the normal of the circular loop and magnetic field is ${90}^{\circ }.$

Flux, $\varphi =\overrightarrow{B}\cdot \overrightarrow{A}$

$\varphi =BA\cos \theta =0[\because \theta ={90}^{\circ }]$

Hence, no magnetic flux is linked with the circular loop due to the current in the long straight wire.

Therefore, the mutual induction between the long straight wire and the circular loop is zero. i.e., $M=\frac{\varphi }{i}=0$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.