Question

A parallel plate capacitor formed by square plates of side length / separated by a distance \( d(d<<1) \) is filled with a material whose dielectric constant varies linearly from \( K \) to \( 2 K \) along \( x \). The capacitance of the capacitor with the dielectric medium will be

Answer 1

For a parallel plate capacitor 

C = \(\cfrac{kɛ_oa}d\)

where K = dielectric constant

ɛ_o = permissivity of free space

a = area of plate

d = distance between the plate

C \(\propto\) K

\(\cfrac{C_1}{C_2}\) = \(\cfrac{k}{2k}\)

= then C₁ = \(\cfrac{C_2}2\)