A parallel-plate capacitor has plates of area \(A\). The plates are initially separated by a distance \(d\), but this distance can be varied. If the capacitor is charged by a battery and the battery is then removed so that the capacitor is isolated, what should the plate separation be if you want to quadruple \((a)\) the capacitance, \((b)\) the charge stored, (c) the energy stored, and (d) the energy density?