A circular coil has a $12\mathrm{.}0$ cm radius and consists of $35\mathrm{.}0$ closely wound turns of wire. An externally produced magnetic field of magnitude $2\mathrm{.}00$ mT is perpendicular to the coil.

$($a$)$ If no current is in the coil, what magnetic flux links its turns?

Wb

$($b$)$ When the current in the coil is $3\mathrm{.}60$ A in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?

H