Question

We use two circular metal plates of radius 0.27 m and thickness 7.9 mm to build a capacitor. We leave a gap of 3.9 mm between the plates and fill half of the space between the plates with a medium with dielectric constant 10.3 and leave the other half filled with air. What is the capacitance of this capacitor?

Hint: you can treat this problem as two capacitors of area A/2 wired in parallel. One is filled with the dielectric medium, and the other with air.

Answer 1

r = radius = 0.27 m

A = Area = $\pi$r² = 3.14 (0.27)² = 0.23 m²

d = width = 0.0039 m

capacitance with air is given as

C₁ = $\epsilon$ A/2d                        eq-1

capacitance with dielectric is given as

C₂ = k$\epsilon$ A/2d                        eq-2

total capacitance is given as

C = C₁ + C₂

C = $\epsilon$ A/2d + k$\epsilon$ A/2d

C = (k + 1) ($\epsilon$ A/2d )

C = (10.3 + 1) (8.85 x 10^-12) (0.23) /(2 x 0.0039) = 2.95 x 10^-9 F