What is the mutual inductance of a two loop system as shown with centre separation $l$ ? (a is radius of the loop)

Magnetic field across coil 1,
$B_1=\frac{{\mu }_{0}i{a}^2}{2{(l^2+a^2)}^{3/2}}$      as  $(1>>a)$

   $B_1=\frac{{\mu }_{0}i{a}^2}{2l^3}$
 Flux induced on coil 2 due to coil 1,
   ${\varphi }_{21}=M{i}_1$
 As we know flux induced on coil 2 due to coil 1.
    ${\varphi }_{21}=B_1{A}_2$
    ${\varphi }_{21}=\frac{{\mu }_{0}i{a}^2}{2l^3}\left(a^2\right)$
    ${\varphi }_{21}=\frac{{\mu }_{0}i{a}^4}{2l^3}=Mi$
Mutual inductance of two loop system   $M=\frac{{\mu }_0{a}^4}{2l^3}$