Find the mutual inductance of two concentric coils of radii `a_(1)` and `a_(2)(a_(1) lt lt a_(2))` if the planes of the coils are perpendicular.

Explanation

If current `i` flows in the larger coil, magnetic field produced at the centre will be perpendicular to the plane of the larger coil. Now, the area vector of the smaller coil which is per pendicular to the plane of the smaller coil will make an angle `theta` with the magnetic field.
Thus, flux `vec(B)*vec(A) = (mu_(0)i)/(2a_(2)) pia_(1)^(2) costheta`
or `M = (mu_(0)pia_(1)^(2) cos theta_(1))/(2a_(2))`