A circuit consists of a parallel-plate capacitor, an inductor, and a switch, which is initially open. The capacitor plates have an area of \(1.00 \times 10^{-4} \mathrm{~m}^{2}\) and are held \(0.100 \mathrm{~mm}\) apart by a thin layer of barium titanate. The capacitor is charged to a potential difference of \(10 \mathrm{~V}\), and then the switch is closed. How much charge remains on the capacitor at the instant the energy stored in the inductor has increased to \(85 \%\) of its maximum?