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:

[math]\displaystyle{ Q_{\mathrm{max}}=4\pi R^2\epsilon_0pE }[/math]

where [math]\displaystyle{ \epsilon_0 }[/math] is the permittivity of free space, [math]\displaystyle{ R }[/math] is the radius of the sphere, [math]\displaystyle{ E }[/math] is the electric field strength, and [math]\displaystyle{ p }[/math] is a material dependent constant.

For conductors, [math]\displaystyle{ p=3 }[/math].

For dielectrics: [math]\displaystyle{ p = 3\epsilon_r/(\epsilon_r + 2) }[/math] where [math]\displaystyle{ \epsilon_r }[/math] is the relative permittivity.

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