JEE Mains · Physics · STD 12 -6. Electromagnetic induction
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 \(M =\frac{\sqrt{2} \mu_0 R ^2}{ L }\)
- B \(M =\frac{2 \sqrt{2} \mu_0 R }{ L ^2}\)
- C \(M =\frac{2 \sqrt{2} \mu_0 R ^2}{ L }\)
- D \(M =\frac{\sqrt{2} \mu_0 R }{ L ^2}\)
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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