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

Answer 1

Answer: (A)

Mutual inductance for two concentric coplanar circular coils,
$\because$ Magnetic flux linked with $A,{\varphi }_A=B\cdot \pi r^2$
$\Rightarrow {\varphi }_A=\frac{{\mu }_{0}I}{2R}\cdot \pi r^2$
$(\because B=\frac{{\mu }_{0}I}{2R}$, magnetic field at the centre of $B$ and $N_1=1=N_2)$
Now, the coefficient $M$;
$\because {\varphi }_A=MI$
$\Rightarrow M=\frac{\frac{{\mu }_{0}I\cdot \pi r^2}{2R}}{I}=\frac{{\mu }_0\pi r^2}{2R}$