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:  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.