Question

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 :

• A. $\frac{{\mu }_0}{4\pi }8\sqrt{2}\frac{a^2}{b}$
• B. $\frac{{\mu }_0}{4\pi }\frac{8\sqrt{2}}{a}$
• C. $\frac{{\mu }_0}{4\pi }8\sqrt{2}\frac{b^2}{a}$
• D. $\frac{{\mu }_0}{4\pi }\frac{8\sqrt{2}}{b}$

Answer 1

Answer: (A)

$B=\left[\frac{{\mu }_0}{4\pi }\frac{I}{b/2}\times 2\sin 45\right]\times 4$
$\varphi =2\sqrt{2}\frac{{\mu }_0}{\pi }\frac{I}{b}\times a^2$
$\therefore M=\frac{\varphi }{I}=\frac{2\sqrt{2}{\mu }_0{a}^2}{\pi b}$
$=\frac{{\mu }_0}{4\pi }8\sqrt{2}\frac{a^2}{b}$