The non-existence of the self-accelerating dipole, and related questions

Abstract

We calculate the self-force of a constantly accelerating electric dipole, showing, in particular, that classical electromagnetism does not predict that an electric dipole could self-accelerate, nor could it levitate in a gravitational field. We also resolve a paradox concerning the inertial mass of a longitudinally accelerating dipole, showing that the combined system of dipole plus field can be assigned a well-defined energy-momentum four-vector, so that the Principle of Relativity is satisfied. We then present some general features of electromagnetic phenomena in a gravitational field described by the Rindler metric, showing in particular that an observer fixed in a gravitational field described by the Rindler metric will find any charged object supported in the gravitational field to possess an electromagnetic self-force equal to that observed by an inertial observer relative to which the body undergoes rigid hyperbolic motion. It follows that the Principle of Equivalence is satisfied by these systems.

10 pages, 4 figures; improved discussion of pressure; added remarks on simultaneity and Rindler frame

References in corpus (2)

• Radiation reaction of a classical quasi-rigid extended particle
• The fields and self-force of a constantly accelerating spherical shell

Cited by in corpus (4)

• Reduced-order Abraham-Lorentz-Dirac equation and the consistency of classical electromagnetism
• Tracking the radiation reaction energy when charged bodies accelerate
• Self-force of a rigid ideal fluid, and a charged sphere in hyperbolic motion
• Electromagnetic self-force for axially symmetric charge on a spherical shell