Question

Two circular coils of radii \(r_1\) and \(r_2\) (\(r_1 \ll r_2\)) are placed coaxially with their centers coinciding. The mutual inductance of the arrangement is:

• A. \( \frac{\mu_0 \pi r_1^2}{2 r_1} \)
• B. \( \frac{\mu_0 \pi r_1 r_2}{2(r_1 + r_2)} \)
• C. \( \frac{\mu_0 \pi r_1^2}{2 r_2} \)
• D. \( \frac{\mu_0 \pi (r_1 + r_2)}{2 r_1 r_2} \)

Hint:

In the case of coaxially placed circular coils with \( r_1 \ll r_2 \), the mutual inductance can be approximated using the formula \( \frac{\mu_0 \pi r_1^2}{2 r_2} \).

Answer 1

The Correct Option is C

The mutual inductance \( M \) between two circular coils is given by: \[ M = \frac{\mu_0 \pi r_1^2}{2 r_2} \] where \( r_1 \) and \( r_2 \) are the radii of the coils, and \( r_1 \ll r_2 \) implies that the first coil is much smaller than the second coil.