Physics

Problem

A parallel-plate capacitor of plate area

A

and separation

d

is completely filled with a homogeneous dielectric material of relative permittivity

\kappa

. The plates carry equal and opposite free charges

\pm Q

. a. (i) Taking the surface charge density on the plates as

\sigma = Q/A

, derive an expression for the magnitude of the electric field inside the dielectric in terms of

\sigma

\varepsilon_0

and

\kappa

. b. (ii) Hence obtain the potential difference

V

between the plates and derive the expression

C = \kappa\varepsilon_0\dfrac{A}{d}

for the capacitance. c. (iii) The capacitor described above has

A = 200\,\text{cm}^2

d = 2\,\text{mm}

and is filled with glass of

\kappa = 5

. Calculate its capacitance in microfarads (

\mu\text{F}