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 :

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Answer & Solution

Correct Answer

(C) \(M =\frac{2 \sqrt{2} \mu_0 R ^2}{ L }\)

Step-by-step Solution

Detailed explanation

\(\phi= Mi\)

\(\phi=( B A )\)

\(\phi=\pi R ^2\left(4 \frac{\mu_0}{4 \pi} \frac{1}{\left(\frac{ L }{2}\right)} \sqrt{2}\right)\)

\(\Rightarrow M =\frac{2 \sqrt{2} \mu_0 R ^2}{ L }\)

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