A laboratory capacitor with fixed plate area and adjustable plate separation is…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A laboratory capacitor with fixed plate area A and adjustable plate separation d is initially charged to a potential difference ΔV0, then disconnected from the charging circuit and isolated so that the charge on each plate remains constant. A researcher wishes to double the energy stored in the capacitor without altering the amount of charge on the plates.
The researcher considers two independent strategies:
• Strategy I: Insert a dielectric material that completely fills the gap while keeping the plate separation fixed.
• Strategy II: Change the plate separation while keeping the gap free of dielectric material.
Edge effects are negligible, and the dielectric constant κ of the available material can be varied by choosing different samples.
(a) For Strategy I, derive an expression for the energy stored after insertion in terms of κ and the initial energy U0. Hence determine the value of κ required to achieve Ufinal=2U0.
(b) For Strategy II, derive an expression for the required final plate separation dfinal in terms of the initial separation d0 such that the stored energy is doubled while the charge remains constant.
(c) Compare the practicality of the two strategies by discussing potential experimental limitations or advantages associated with each approach.