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
The next part uses the preceding result as input rather than treating parts independently. This keeps conventions and physical state consistent throughout.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.