Question

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:

• A. $\frac{\mu_0 \pi a^2}{2b}$
• B. $\frac{\mu_0}{2\pi} \cdot \frac{b^2}{a}$
• C. $\frac{\mu_0 \pi b^2}{2a}$
• D. $\frac{\mu_0}{2\pi} \cdot \frac{a^2}{b}$

Answer 1

Answer: (A)

$\frac{\mu_0 \pi a^2}{2b}$

Answer 2

The magnetic flux ($\phi$) through loop B due to current in loop A is given by:

$\phi = M \cdot i = B \cdot A$

The mutual inductance is:

$M = \frac{\mu_0 \pi a^2}{2b}$

where $a$ is the radius of loop A, $b$ is the distance between the loops, and $\mu_0$ is the permeability of free space.