Problem 2
A parallel-plate capacitor of initial capacitance C is charged to V₀ and then completely disconnected from its source and leads. A linear dielectric of relative permittivity κ>1 is inserted to fill the gap; neglect fringing and assume the plates do not move. (a) Find initial charge Q₀, which remains conserved during insertion. (b) Calculate final capacitance and voltage V_f. (c) Compare initial and final field energies and state the work done by an external agent in slow insertion. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
First identify the system, given quantities, and sign convention; this determines what is conserved or acts on the body. The stated idealizations exclude unmentioned forces or effects.