Instability of dielectrics and conductors in electrostatic fields

Preprint English OPEN
Allaire, Grégoire; Rauch, Jeffrey;
  • Publisher: HAL CCSD
  • Subject: Dirichlet's Theorem | electromagnetism | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | Instability | 70H14, 35B35, 35Q60, 35Q61, 35Q70, 70E91 | perfect conductor | [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] | dielectric | Earnshaw's Theorem
    arxiv: Physics::Classical Physics

This article proves most of the assertion in §116 of Maxwell's treatise on electromagnetism. The results go under the name Earnshaw's Theorem and assert the absence of stable equilibrium configurations of conductors and dielectrics in an external electrostatic field.
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