Question

$O$ is the centre of two coplanar concentric circular conductors $A$ and $B$, of radii $r$ and $R$ respectively as shown in the figure. Here, $r <<< R$. The mutual inductance of the system of the conductor can be given by

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

Answer 1

Answer: (A)

Mutual inductance for two concentric coplanar circular coils,
$\because$ Magnetic flux linked with $A, \phi_{A}=B \cdot \pi r^{2}$
$\Rightarrow \phi_{A}=\frac{\mu_{0} I}{2 R} \cdot \pi r^{2}$
$(\because B=\frac{\mu_{0} I}{2 R}$, magnetic field at the centre of $B$ and $\left.N_{1}=1=N_{2}\right)$
Now, the coefficient $M$;
$ \because \phi_{A} =M I $
$ \Rightarrow M =\frac{\frac{\mu_{0} I \cdot \pi r^{2}}{2 R}}{I}=\frac{\mu_{0} \pi r^{2}}{2 R} $