PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two identical parallel-plate capacitors, each of plate area A and plate separation d, are prepared for a classroom demonstration. In both cases the initial state is an empty gap (air, κ=1) between the plates.
• In Case 1, the capacitor is connected to a battery that maintains a constant potential difference ΔV0 across the plates. While the battery remains connected, a dielectric slab with constant κ>1 completely fills the space between the plates.
• In Case 2, a second, identical capacitor is charged to the same initial potential difference ΔV0, disconnected from the battery so that its charge remains constant, and then the same type of dielectric slab is inserted to fill the gap.
Assume edge effects are negligible.
(a) For Case 1, describe qualitatively how the magnitude of (i) the charge on the plates, (ii) the electric field between the plates, and (iii) the energy stored in the capacitor change after the dielectric is fully inserted. Explain your reasoning for each quantity.
(b) For Case 2, answer the same three questions—how do the charge magnitude, electric field, and stored energy change after insertion? Provide explanations.
(c) Comparing the two cases, indicate in which case an external agent must supply positive mechanical work during the insertion process. Justify your answer in terms of energy conservation.