Question

Find the appoximate formula expressing the mutual inductance of two thin coaxial loops of the same radius `a` if their centres are separated by a distance `l`, with `l gt gt a`

Answer 1

If a current `I` flows is one of the coils, the magnetic field at6 the centre of the other coil is,
`B = (mu_(0) a^(2) I)/(2(l^(2) + a^(2))^(3//2)) = (mu_(0) a^(2) I)/(2 l^(3))`, as `l gt gt a`
The flux associated with the secound coil is then appoximately `mu_(0) pi a^(4) I//2 l^(3)`
Hence, `L_(12) = (mu_(0) pi a^(4))/(2 l^(3))`