$2.(20$ marks$)$ A magnetic circuit is shown in Fig. $2,$ in which the left and right branch have an air gap with a height of $5$ cm $.$ The steel frame material has $\backslash (\backslash$mu$\_\{$r$\}=\backslash$infty $.\backslash$mathrm$\{$N$\}=100\backslash )$ and the current $\backslash (\backslash$mathrm$\{$I$\}=5\backslash$mathrm$\{$~A$\}\backslash ).$ Find

a$)$ The total reluctance and equivalent circuit

b$)$ The flux density B across the air gap

c$)$ The total inductance L

d$)$ The stored energy in the air gap