Q$4)$ A transformer core has a mean path length of $0\mathrm{.}5$ m and a cross$-$sectional area of $0\mathrm{.}01m^2.$ The core material has a relative permeability of $2,500.$ If the transformer has $300$ turns and carries a current of $1$ A $,$ calculate:

$($a$)$ The reluctance of the core.

$($b$)$ The magnetomotive force $($MMF$).$

$($c$)$ The flux through the core.