A parallel-plate capacitor initially filled with air ( ) has plate area and plate…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A parallel-plate capacitor initially filled with air (κ=1) has plate area 0.020m2 and plate separation d=3.0mm. A solid glass slab with dielectric constant κ=5.0 is slowly inserted from one plate until it completely fills exactly half of the separation, leaving the other half as air. During the insertion, the capacitor is isolated so that the total free charge on each plate remains constant at Q=8.0nC.
Throughout this question, ignore edge effects.
(a) Model the resulting system as two capacitors connected in series. Derive an expression for the equivalent capacitance in terms of κ, ε0, A, and d.
(b) Using the given numerical values, calculate the equivalent capacitance after the glass is fully inserted halfway.
(c) Determine the potential difference across the entire set of plates and the magnitude of the electric field within (i) the glass region and (ii) the air region.
(d) If the free charge Q were gradually increased while the geometry remained fixed, which region—glass or air—would reach electrical breakdown first? Justify your answer using the fields found in part (c) and typical breakdown strengths for the two materials.