Question

Two conducting circular loops of radii $R_{1}$ and $R_{2}$ are placed in the same plane with their centres coinciding. If $R_{1}>>R_{2}$, the mutual inductance $M$ between them will be directly proportional to:

• A. $\frac{ R _{1}}{ R _{2}}$
• B. $\frac{R_{2}}{R_{1}}$
• C. $\frac{ R _{1}^{2}}{ R _{2}}$
• D. $\frac{ R _{2}^{2}}{ R _{1}}$

Answer 1

Answer: (D)

Magnetic field due to $R_{1}$ at the center
$B=\frac{\mu_{0} i}{2 R_{1}}$
Flux linked with $R_{2}$
$\phi= BA _{2}=\frac{\mu_{0} i }{2 R _{1}} \times \pi R _{2}^{2}= Mi$
$M=\frac{\mu_{0} \pi R_{2}^{2}}{2 R_{1}} $
$M \propto \frac{R_{2}^{2}}{R_{1}}$