Question

What is the mutual inductance of a two-loop system as shown with centre separation l

• A. $\frac{{\mu }_o\pi a^4}{8l^3}$
• B. $\frac{{\mu }_o\pi a^4}{4l^3}$
• C. $\frac{{\mu }_o\pi a^4}{6l^3}$
• D. $\frac{{\mu }_o\pi a^4}{2l^3}$

Answer 1

The correct option is D $\frac{{\mu }_o\pi a^4}{2l^3}$

Magnetic field at the location of coil (2) produced due to coil (1)
$B_1=\frac{{\mu }_o}{4\pi }.\frac{2M}{l^3}$
Flux linked with coil (2)
${\varphi }_2=B_1{A}_2=\frac{{\mu }_o}{4\pi }\frac{2i\left(\pi a^2\right)}{l^3}\times \left(\pi a^2\right)$

Also ${\varphi }_2=M_i\Rightarrow M=\frac{{\mu }_o\pi a^4}{2l^3}$