Magnetic field produced by a current i in a large square loop at its centre,

B ∝ $\genfrac{}{}{0.1ex}{}{i}{L}$

Say  B = K $\genfrac{}{}{0.1ex}{}{i}{L}$
 
 Therefore, Magnetic flux linked with smaller loop,
     ϕ=B. S                                               '
     ϕ = k $\genfrac{}{}{0.1ex}{}{i}{L}$(/²)
Therefore, the mutual inductance

M =$\genfrac{}{}{0.1ex}{}{\mathrm{\ϕ}}{i}$= K$\genfrac{}{}{0.1ex}{}{l^2}{L}$  
 
or         M ∝$\genfrac{}{}{0.1ex}{}{l^2}{L}$