# The effect of an electric field on capacitance

Decreasing the distance between the two parallel plates of a capacitor increases the amount of charge that can be held on each plate. If this is because the charges are attracted to each other and consequently less "focused" on repelling like charges, why do dielectrics increase capacitance?

Wouldn't the electric fields, which face the opposite direction, caused by the dipoles of the atoms of the dielectric decrease the electric field between plates and as a consequence this attractive force?

And if so, does that mean that the charge-dielectric dipole attraction has a greater effect than the original electric field between plates (without a dielectric)?

Assume that the voltage across an isolated capacitor with air ($\approx$ vacuum) between the plates of separation $d$ is $V_{\text{air}}$ and the charge stored on the capacitor is $Q$.

$Q = C_{\text{air}} V_{\text{air}}$

The electric field between the plates is $E_{\text{air}} = \dfrac {V_{\text{air}}} {d}$.

Now put a dielectric of relative permittivity $\epsilon_r$ between the plates.
Charges are induced in the dielectric which produce an electric field in opposition to the electric field produced by the charges on the plates.

The net electric field between the plates decreases as does the force between the plates and the electric field becomes $\dfrac {E_{\text{air}}}{\epsilon_r}$

This in turn means that the potential difference across the plates must also be reduced to $\dfrac {V_{\text{air}}}{\epsilon_r}$

The charge on the capacitor $Q$ is still the same so the capacitance of the capacitor has incresed and is now $\epsilon_r C_{\text{air}}$.

• And for added fun, the dielectric constant of materials changes depending on voltage (which is usually ignored) – user56903 May 3 '16 at 10:53
• @DirkBruere Does the dielectric constant change by much? – Farcher May 3 '16 at 12:28

Wouldn't the electric fields, which face the opposite direction, caused by the dipoles of the atoms of the dielectric decrease the electric field between plates and as a consequence this attractive force

Yes it would. This means that you can increase the voltage if you want. And thus get more charge stored on the capacitor plates before they are filled up (before the same electric field has been established).

This is what is meant by capacity: its ability to store charge before being "full". And since a dielectric reduced the effect of the stored charge, the "fullness" is decreased corresponding to a larger capacity.