Electrostatics: variable permittivity dielectric capacitor.
October 11th, 2022
The relative permittivity of the dielectric between the plates of a parallel plate capacitor varies linearly from one plate to the other. If epsilon_r1 and epsilon_r2 are the values at the two plates, where epsilon_r2>epsilon_r1, and if the plate separation is s, show that the capacitance per unit area is
[epsilon_o(epsilon_r2 – epsilon_r1)]/ s ln (epsilon_r2/epsilon_r1).