Question 86: Electromagnetic Induction

Question

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire $$\mathrm{L}(\mathrm{L}>>l)$$. Both loops are coplanar and their centres coincide at point $$\mathrm{O}$$ as shown in figure. The mutual inductance of the system is :

Accepted Answer

We know $$\phi  = Mi$$
Let i current be flowing in the larger loop
$$ \Rightarrow \phi  \simeq \left[ {4 	imes {{{\mu _0}i} \over {4\pi (L/2)}}[\sin 45^\circ  + \sin 45^\circ ]} ight] 	imes $$ Area
$$ = {{2\sqrt 2 {\mu _0}i} \over {\pi L}} 	imes {I^2}$$
$$ \Rightarrow M = {\phi  \over i} = {{2\sqrt 2 {\mu _0}{I^2}} \over {\pi L}}$$

Answer

$$\frac{2 \sqrt{2} \mu_{0} \mathrm{~L}^{2}}{\pi l}$$

Answer

$$\frac{\mu_{0} l^{2}}{2 \sqrt{2} \pi \mathrm{L}}$$

Answer

$$\frac{2 \sqrt{2} \mu_{0} l^{2}}{\pi \mathrm{L}}$$

Answer

$$
\frac{\mu_{0} \mathrm{~L}^{2}}{2 \sqrt{2} \pi l}
$$

Electromagnetic Induction

A small square loop of wire of side $l is placed inside a large square loop of wire \mathrm{L}(\mathrm{L}>>l). Both loops are coplanar and their centres coincide at point \mathrm{O}$ as shown in figure. The mutual inductance of the system is :

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