Question

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

• A. $\frac{\mu_{0} \pi a^{4}}{8 l^{3}}$
• B. $\frac{\mu_{0} \pi a^{4}}{4 l^{3}}$
• C. $\frac{\mu_{0} \pi a^{4}}{6 l^{3}}$
• D. $\frac{\mu_{0} \pi a^{4}}{2 l^{3}}$

Answer 1

Answer: (D)

Magnetic field at the location of coil (2) produced due to coil $(1)$

$B_{1}=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 M}{l^{3}}$
Flux linked with coil (2),
$\phi_{2}=B_{1} A_{2}=\frac{\mu_{0}}{4 \pi} \frac{2 i\left(\pi a^{2}\right)}{l^{3}} \times\left(\pi a^{2}\right)$
Also, $\phi_{2}=M i \Rightarrow M=\frac{\mu_{0} \pi a^{4}}{2 l^{3}}$