Question

Two concentric co-planar circular loops of radius $R$ and $r\left( < < R\right)$ are placed as shown in the figure. The mutual inductance of the system will be

• A. $\frac{\pi \mu _{0} r^{2}}{2 R}$
• B. $\frac{\pi \mu _{0} r^{2}}{4 R}$
• C. $\frac{\pi \mu _{0} R^{2}}{4 r}$
• D. $\frac{\pi \mu _{0} R^{2}}{2 r}$

Answer 1

Answer: (A)

The magnetic flux through the smaller loop due to the bigger loop is
$\left(\phi\right)_{21}=\left(\frac{\left(\mu \right)_{0} i}{2 R}\right)\times \pi r^{2}$
$\Rightarrow M=\frac{\left(\phi\right)_{21}}{i}=\left(\frac{\pi \left(\mu \right)_{0} r^{2}}{2 R}\right)$