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  4. A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn ( b >> a ). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is :

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Q. A small square loop of side '$a$' and one turn is placed inside a larger square loop of side b and one turn $( b >> a )$. The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side '$b$', then the coefficient of mutual inductance between the two loops is :

JEE MainJEE Main 2021Electromagnetic Induction

Solution:

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$B =\left[\frac{\mu_{0}}{4 \pi} \frac{ I }{ b / 2} \times 2 \sin 45\right] \times 4$
$\phi=2 \sqrt{2} \frac{\mu_{0}}{\pi} \frac{ I }{ b } \times a ^{2}$
$\therefore M=\frac{\phi}{I}=\frac{2 \sqrt{2} \mu_{0} a^{2}}{\pi b}$
$=\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{a^{2}}{b}$