A circular coil has a $2\mathrm{.}15$ cm radius and consists of $78$ closely wound turns of wire. A uniform external magnetic field of magnitude $29\mathrm{.}4$ mT is perpendicular to the plane of the coil. When the current in the coil is $3\mathrm{.}05$ A $,$ the net flux through the coil is found to vanish. What is the inductance of the coil?

$($A$)2\mathrm{.}18$ mH

$($B$)3\mathrm{.}71{10}^{-2}mH$

$($C$)1\mathrm{.}09$ mH

$($D$)752$ mH

$($E$)11\mathrm{.}1$ mH