Question

A parallel plate capacitor has a rectangular plates of side length a and b, which are seperated y a distance of d. A dielectric of relative permittivity $\epsilon_r$ is placed between the plates such that in one direction, x, it omplteley overlaps the plates (x=a) but in the orthgonal diection it only over lps a distance y(y<b). Air still occupies the region of the area a(b-y).

If the capacitor is maibtained with a constant charge of Q. Show that the energy ,U, of the system is:

$U=\frac{Q^2d}{2\epsilon_0a[b-y+y\epsilon_r]}$

Addtionla information no external voltage is applied.

Answer 1

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