Two identical circular metal plates

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Two identical circular metal plates, each of radius

r

, are kept parallel to each other in air at a separation

d

such that

r \gg d

. (i) Derive an expression for the capacitance

C

of this arrangement in terms of

r

d

, and

\varepsilon_0

. (ii) Two such capacitors are connected in parallel. Show that the equivalent capacitance is twice that of a single capacitor. (iii) For

r = 5.0\,\text{cm}

and

d = 1.0\,\text{mm}

, calculate the equivalent capacitance obtained in part (ii). Use

\varepsilon_0 = 8.85 \times 10^{-12}\,\text{C}^2\,\text{N}^{-1}\,\text{m}^{-2}

. (iv) Keeping

r

unchanged, the separation

d

is reduced by

20\%

. Calculate the percentage change in the equivalent capacitance found in part (ii).