A spherical capacitor has an inner radius of \(5 \mathrm{~cm}\) and an outer radius of \(6 \mathrm{~cm}\). With air between the spheres, the capacitor is connected to a \(12-\mathrm{V}\) battery and allowed to charge fully. With the battery still connected, oil \((\kappa=2.2\) is poured in, filling the volume between the spheres. Calculate the additional work done by the battery throughout the process of filling the capacitor with oil.,\(\infty\).