Pauthenier equation
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The Pauthenier equation states [1][2] 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.
References
[edit]- ^ Goldwater, Daniel; Millen, James (2019). "Levitated electromechanics: all-electrical cooling of levitated nano- and micro-particles". Quantum Science and Technology. 4: 024003. arXiv:1802.05928. doi:10.1088/2058-9565/aaf5f3. S2CID 119244999.
- ^ K. Adamiak, "Rate of charging of spherical particles by monopolar ions in electric fields", IEEE Transactions on Industry Applications 38, 1001-1008 (2002)