Answer to Question #136892 in Electricity and Magnetism for mpho

Question

"A fixed voltage is connected across parallel plate capacitor. Does the electric field intensity in the space between the plates depends on permittivity of the medium? Does the electric flux density depends upon the permittivity of the medium?

Answer 1

The capacitance C of the plate capacitor depends on the charge Q on the plates of the capacitor and the voltage V as $C = \dfrac{Q}{V}.$

For a parallel-plate capacitor the difference of potentials V is $V = \dfrac{Qd}{\varepsilon A},$ where A is the area of plate, $\varepsilon$ is the permittivity and d is the distance between the plates (see https://en.wikipedia.org/wiki/Capacitor#Parallel-plate_capacitor), so the capacitance is $C={\varepsilon A \over d}$ .

According to (https://en.wikipedia.org/wiki/Capacitor#Parallel-plate_capacitor), the voltage between two plates on the distance d is V = Ed, so if the voltage is constant, the intensity E does not depend on permittivity (but Q does).

The electric flux density is $D=\varepsilon E.$ Therefore, if in our case E is independent of the permittivity, D is dependent on it.

Maybe it'll be useful to compare the situation in question and the explanation of the situation with constant charge on the plates: https://www.therightgate.com/electric-flux-density-d/