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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