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