$-41$ A circular coil has a $10\mathrm{.}0cm$ radius and consists of $30\mathrm{.}0$ closely wound turns of wire. An externally produced magnetic field of magnitude $2\mathrm{.}60mT$ is perpendicular to the coil. $($a$)$ If no current is in the coil, what magnetic flux links its turns? $($b$)$ When the current in the coil is $3\mathrm{.}80A$ in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?