The approximate formula expressing the inductance of two thin co-axial loops of the same radius a when  their centres are separated by a distance l with l > > a is

Let I = current in one loop. This magnetic flux at the centre of the other co-axial loop at a distance l from the centre of the first loop isB=μ04π2I.πa2a2+ℓ23/2The flux through the other loop isϕ12=Bπa2=μ04π⋅2πa2Ia2+ℓ23/2πa2 or ϕ12I=μ04π⋅2π2a42a2+ℓ23/2=ϕ0πa42a2+ℓ23/2∴μ12=M12IM12=ϕ12I=12μ0πa4ℓ3(∵a<<ℓ)