A parallel-plate air capacitor with plate area and initial plate separation is…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A parallel-plate air capacitor with plate area A=0.015m2 and initial plate separation d0=2.0mm is charged by an ideal 500 V battery and then disconnected so that the charge on the plates remains fixed. The plates are then slowly pulled apart until the separation doubles to 2d0=4.0mm. Edge effects are negligible.
(a) Derive an expression for the energy stored in the capacitor as a function of plate separation s (with d0≤s≤2d0) while the charge remains constant.
(b) Calculate the initial energy stored when the separation is d0.
(c) Calculate the final energy stored after the separation has doubled.
(d) Determine the mechanical work required to pull the plates apart from d0 to 2d0. State whether this work must be supplied by the external agent or whether the plates would tend to move apart on their own, and justify your answer based on energy considerations.