A 2.0μF parallel-plate capacitor is connected across a 12V battery until it is fully charged. The battery is then disconnected, leaving the capacitor isolated. A dielectric material that completely fills the space between the plates is next inserted. The dielectric constant of the material is κ=4.0. Neglect fringe effects.
(a) Calculate the magnitude of the charge on each plate before the dielectric is inserted.
(b) Determine the potential difference across the plates after the dielectric has been inserted.
(c) Compute the energy stored in the capacitor both before and after the insertion of the dielectric. State whether external work must be done on the system during the insertion and explain your reasoning.