An insulating gas or solid can support an electric field only up to a finite range of operating conditions. If the field becomes strong enough, initially scarce mobile charges can multiply and the material can suddenly become much more conductive. This transition is electrical breakdown.

Acceleration of free charges

A free charge $q$ in an electric field experiences force

$$\mathbf F=q\mathbf E.$$

Between collisions, an electron can gain kinetic energy from the field. If a collision transfers enough energy to an atom or molecule, it can remove a bound electron and create an ion-electron pair. This process is impact ionization.

The newly freed electron can itself be accelerated and ionize another particle. Repetition produces an avalanche of charge carriers.

The current can then increase rapidly even though the material was initially a good insulator.

Breakdown field

A material is often characterized approximately by a breakdown field $E_{\rm bd}$: an electric-field magnitude above which breakdown becomes likely for the specified geometry and conditions.

For an approximately uniform field across a gap of width $d$, a rough voltage scale is

$$\boxed{V_{\rm bd}\approx E_{\rm bd}d}.$$

This is not a universal constant relation. Breakdown depends on material composition, pressure, temperature, gap size, electrode shape, surface condition, impurities, and the duration of the applied field.

Why sharp conductors promote breakdown

In electrostatic equilibrium, surface charge tends to become more concentrated near regions of high curvature such as sharp points. The local electric field can therefore be much larger near a sharp electrode than the average field inferred from the overall voltage and spacing.

Breakdown often begins at such high-field regions. This is one reason high-voltage equipment avoids unnecessarily sharp conducting features.

Spark formation in a gas

Once an avalanche creates enough charge carriers, the ionized path through a gas can conduct strongly. Energy deposited in the gas can heat it and produce light, creating a visible spark or discharge channel.

A spark is therefore not charge 'jumping through empty space' without a mechanism. The strong field creates and accelerates mobile carriers in matter that was previously only weakly conducting.

After the field collapses or the source is removed, electrons and ions can recombine or be collected at boundaries, so the gas can return toward an insulating state.

Worked example

Suppose a particular insulating gap can be modeled with

$$E_{\rm bd}=3.0\times10^6,\mathrm{V/m}$$

under the stated conditions, and the approximately uniform gap is

$$d=2.0,\mathrm{mm}=2.0\times10^{-3},\mathrm m.$$

The corresponding breakdown-voltage estimate is

$$V_{\rm bd}\approx E_{\rm bd}d =(3.0\times10^6)(2.0\times10^{-3}) =6.0\times10^3,\mathrm V.$$

Thus

$$\boxed{V_{\rm bd}\approx6.0,\mathrm{kV}}.$$

The calculation is only an estimate because real breakdown fields depend strongly on the physical conditions and field geometry.

Breakdown is a limit of electrostatic component models

Ideal capacitor and dielectric equations assume that the insulating region remains insulating. Once breakdown occurs, substantial conduction can redistribute charge and dissipate stored field energy, so the original electrostatic model is no longer sufficient.

Electrical breakdown is therefore both a microscopic ionization process and a practical operating limit for capacitors, insulators, cables, semiconductor devices, and high-voltage systems.