Two circular coils, one of radius r and the other of radius R are placed co-axially with their centres coinciding - Physics - Electromagnetic Waves

Question

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

Vara · Accepted Answer

Let
R = Radius of the first coil
r = Radius of the second coil
I = Current through the first coil

Magnetic field at the centre of the first coil:

B=μ0I2RMagnetic flux linked with second coil is,ϕ=BA   =μ0I2R×πr2Mutula inductance:M=ϕI    =μ02R×πr2     =μ0πr22R

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