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Electrostatics: variable permittivity dielectric capacitor.

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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).

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Solution Summary

The permittivity of the dielectric slab in a parallel plate capacitor is varying linearly. The capacitance per unit area is determined.

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