\(B=\frac{\mu_{0} N i}{2 \pi R}\)

The expression for the magnetic flux is,

\(\phi_{\text {self }}=B A N\)

\(=\frac{\mu_{0} N i}{2 \pi R} A N\)

\(=\frac{\mu_{0} N^{2} i A}{2 \pi R}\) \(...(1)\)

Also, the expression for magnetic flux in terms of inductance is,

\(\phi_{\text {self }}=L i\) \(...(2)\)

Equate equation \((1)\) and \((2)\)

\(L=\frac{\mu_{0}}{2 \pi} \frac{N^{2} A}{R}\)

Substitute the values in the above equation.

\(L=\left(10^{-7}\right) \frac{2 \times 500^{2} \times 10 \times\left(10^{-2}\right)^{2}}{0.4}\)

\(=125 \mu H\)