Physics:Pauthenier equation

The Pauthenier equation states that the maximum charge accumulated by a particle modelled by a small sphere passing through an electric field is given by:

$Q_{\mathrm{m}\mathrm{a}\mathrm{x}}=4\pi R^2{ϵ}_{0}pE$

where ${ϵ}_0$ is the permittivity of free space, $R$ is the radius of the sphere, $E$ is the electric field strength, and $p$ is a material dependent constant.

For conductors, $p=3$.

For dielectrics: $p=3{ϵ}_r/({ϵ}_r+2)$ where ${ϵ}_r$ is the relative permittivity.

Low charges on nanoparticles and microparticles are stable over more than 10³ second time scales.