Problem 2
A parallel-plate capacitor of capacitance (air-filled) is charged to voltage then disconnected from the source. A dielectric slab of constant is then inserted, filling the gap. Find the capacitor's energy before and after insertion, and explain the change. (a) Find plate charge, capacitance after insertion, and final voltage. (b) Calculate initial and final field energies and their ratio in terms of . (c) Explain the mechanical work associated with the energy decrease as the slab is drawn in; distinguish field work from external work and state what is conserved after disconnection.
problems.proof.stepOf
problems.proof.analysis
The dielectric is pulled toward stronger field, so field work is positive; an agent controlling quasistatic insertion does opposite work. The energy decrease becomes mechanical energy, not a loss.