Question 66: Electromagnetic Induction

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 :

Accepted Answer

$
\begin{aligned}
& B 	ext { at centre }=\frac{\mu_{0} i}{4 \pi\left(\frac{L}{2}ight)}\left(\frac{2}{\sqrt{2}}ight) 	imes 4 \\
&= \frac{\sqrt{2} \mu_{0} i}{2 \pi L} 	imes 4 \\
&=\left(\frac{2 \sqrt{2} \mu_{0} i}{\pi L}ight)
\end{aligned}
$
Mutual inductance $=\frac{B \cdot A}{i}$
$
=\frac{2 \sqrt{2} \mu_{0} i}{\pi L} 	imes \frac{\pi R^{2}}{i}
$
$
=\left(\frac{2 \sqrt{2} \mu_{0} R^{2}}{L}ight)
$

Answer

$M=\frac{\sqrt{2} \mu_{0} R}{L^{2}}$

Answer

$M=\frac{2 \sqrt{2} \mu_{0} R}{L^{2}}$

Answer

$M=\frac{2 \sqrt{2} \mu_{0} R^{2}}{L}$

Answer

$M=\frac{\sqrt{2} \mu_{0} R^{2}}{L}$

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 :

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