A spherical capacitor has an inner radius of 8.00 mm and an outer radius of 8.50 mm. With air between the spheres, the capacitor is connected to a...

A spherical capacitor has an inner radius of 8.00 mm and an outer radius of 8.50 mm. With air between the spheres, the capacitor is connected to a battery and allowed to charge fully. With the battery still connected, oil is poured in, filling the volume between the spheres. As the oil is added, the battery does an additional 8.50 nJ of work on the capacitor. Suppose that the dielectric constant of the oil is κoil = 4.5. What is the potential difference supplied by the battery?