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:
where is the permittivity of free space, is the radius of the sphere, is the electric field strength, and is a material dependent constant.
For conductors,.
For dielectrics: where is the relative permittivity.
Low charges on nanoparticles and microparticles are stable over more than 103 second time scales.