Permitivity $\mathcal{E}$ as a function of Voltage across a medium

What I wanted to Know was is there a change in Dielectric Permitivity constant as the voltage increases. My question arose from the fact that for a breakdown voltage to be reached the Permitivity constant $\mathcal{E}_0$ must be a function of voltage.

Meaning that the Capacitance of a capacitor must change as the voltage increases across it .
Further Meaning that the charge as a function of voltage must not be linear for a capacitor (paralell plate).

If it isn't then the capacitance of a capacitor would also depend on the voltage across it.

So all my above questions boil down to one single question :

Is the Permitivity Constant $\mathcal{E}$ of a dielectric medium Voltage dependent ?

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Generally speaking the permittivity is not voltage dependant for voltages up to a substantial fraction of the breakdown voltage. So the capacitance of a capacitor is not voltage dependant.

Dielectric breakdown usually occurs due to some major change in the structure of the dielectric. The most obvious example is lightening. The permettivity of air is not voltage dependant until the field strength gets high enough to ionise the air, at which point the permittivity changes completely and you get a lightening bolt. Likewise, in a typical capacitor of the type used in your TV at some voltage a high enough voltage will rip electrons free in the dielectric and you'll get a current flowing between the plates.

In both cases this isn't really a voltage dependence of the permittivity but rather a change in state of the dielectric that produces a new permittivity.

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Permitivity $\epsilon$ depends weakly on the voltage, but it has two parts - a real one and an imaginary one. The imaginary part determines the conductivity (or resistance, if you like) of dielectric. Normally the resistance is chosen very high.

For too high voltages the current may become sufficiently high to modify physical properties of the dielectric and cause its breakdown.

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