Question

Two circular coils, one of radius r and other of radius R are placed coaxially with their centres coinciding. For R >> r, obtain an expression for mutual inductance of the arrangement.

Answer 1

If i is the current passing in the outer coil of radius R, then magnetic field at its centre.

B = \(\frac{\mu_0}{4\pi} \frac{2\pi i}{R}\)

∴ Magnetic flux through coil P

Φ = BA = \(\frac{\mu_0}{4\pi} .\frac{2\pi i}{R}(\pi r^2)\)

= \(\frac{\mu_0}{4\pi} .\frac{2\pi^2 ir^2}{R}\)

∴ mutual inductance between the coils

M = \(\frac{\phi}{i} = \) \(\frac{\mu_0}{4\pi} \frac{2\pi^2 r^2}{R}\)