Example

As shown, a ring type core has a circular cross section with $1\mathrm{.}5$ cm radius and mean length of circumference is $60$ cm $.$ The ring is wound with a $800$ turn coil and has an airgap of $1$ mm $.$

$($a$)$ Calculate the current in the coil to establish a flux of $0\mathrm{.}8$ mWb in the airgap. Neglect leakage and fringing. The magnetization curve points of the core are provided in the table.

$($b$)$ Calculate the flux in the core when $1\mathrm{.}2$ A current flows in the coil.