Question

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' $R$ ' is placed inside a large square loop of wire of side $L$ $(L \gg R)$. The loops are coplanar and their centres coincide:

• A. $M=\frac{2 \sqrt{2} \mu_0 R^2}{L}$
• B. $M=\frac{\sqrt{2} \mu_0 R^2}{L}$
• C. $M=\frac{2 \sqrt{2} \mu_0 R}{L^2}$
• D. $M=\frac{\sqrt{2} \mu_0 R}{L^2}$

Answer 1

Answer: (A)

$ \phi= Mi $
$ \phi=( BA )$
$ \phi=\pi R ^2\left(4 \frac{\mu_0}{4 \pi} \frac{ i }{\left(\frac{ L }{2}\right)} \sqrt{2}\right)$
$ \Rightarrow M =\frac{2 \sqrt{2} \mu_0 R ^2}{ L }$