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Earnshaw’s Theorem in Electrostatics
PDE and Applied Math Seminar| Speaker: | Jeffrey Rauch, University of Michigan |
| Location: | zoom |
| Start time: | Thu, Feb 25 2021, 4:10PM |
This result dating to 1842 asserts that a charge in a static
electrostatic field can never be in a stable equilibrium. In
spite of many partial results a complete proof was first
given in 1987. The present talk concerns generalizations
from Section 116 of Maxwell’s treatise. There Maxwell
explains why a rigid charged body or a perfect conducting
body or a dielectric body in a static field can never be
in a stable equilibrium. We prove the result for conductors
and dielectrics. The charged rigid body remains open.
This joint work with G. Allaire appeared in the Archive
for Rational Mechanics in 2017.