Flux linkage for inner loop. $$ \begin{aligned} & \phi=\mathrm{B}_{\text {center }} \cdot \ell^2 \\ & =4 \times \frac{\mu_0 \mathrm{i}}{4 \pi \frac{\mathrm{~L}}{2}}(\sin 45+\sin 45) \ell^2 \\ & \phi=2 \sqrt{2} \frac{\mu_0 \mathrm{i}}{\pi \mathrm{~L}} \ell^2 \\ & \mathrm{M}=\frac{\phi}{\mathrm{i}}=\frac{2 \sqrt{2} \mu_0 \ell^2}{\pi \mathrm{~L}}=2 \sqrt{2} \frac{\mu_0}{\pi} \\ & =2 \sqrt{2} \frac{4 \pi}{\pi} \times 10^{-7} \\ & =8 \sqrt{2} \times 10^{-7} \mathrm{H} \\ & =\sqrt{128} \times 10^{-7} \mathrm{H} \\ & \mathrm{x}=128 \end{aligned} $$