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:
formula_1
where formula_2 is the permittivity of free space, formula_3 is the radius of the sphere, formula_4 is the electric field strength, and formula_5 is a material dependent constant.
For conductors, formula_6.
For dielectrics: formula_7 where formula_8 is the relative permittivity.
Low charges on nanoparticles and microparticles are stable over more than 103 second time scales.
References.
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