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 conductors 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)

$\frac{{\mu }_0\pi r^2}{2R}$

Mutual inductance for two concentric coplanar circular coils,

$M=\frac{\pi {\mu }_0{N}_1{N}_2{r}^2}{2R}$

Here, $N_1=N_2=1$

$\therefore M=\frac{\pi {\mu }_0{r}^2}{2R}$.