dorsal/arxiv
View SchemaDerivation of the potential, field, and locally-conserved charge-current density of an arbitrarily moving point-charge
| Authors | Andre Gsponer |
|---|---|
| Categories | |
| ArXiv ID | physics/0612232 |
| URL | https://arxiv.org/abs/physics/0612232 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. The current density includes, apart from the well-established three-dimensional delta-function which is sufficient for its global conservation, additional delta-contributions depending on the second and third proper-time derivatives of the position, which are necessary for its local conservation as required by the internal consistency of classical electrodynamics which implies that local charge-conservation is an {identity}. Similarly, the field strength includes an additional delta-contribution which is necessary for obtaining this result. The Lienard-Wiechert field and charge-current density must therefore be interpreted as nonlinear generalized functions, i.e., not just as distributions, even though only linear operations are necessary to verify charge-current conservation. The four-potential from which this field and the conserved charge-current density derive is found to be unique in the sense that it is the only one reducing to an invariant scalar function in the instantaneous rest frame of the point-charge that leads to a point-like locally-conserved charge-current density.
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"abstract": "The complete charge-current density and field strength of an arbitrarily\naccelerated relativistic point-charge are explicitly calculated. The current\ndensity includes, apart from the well-established three-dimensional\ndelta-function which is sufficient for its global conservation, additional\ndelta-contributions depending on the second and third proper-time derivatives\nof the position, which are necessary for its local conservation as required by\nthe internal consistency of classical electrodynamics which implies that local\ncharge-conservation is an {identity}. Similarly, the field strength includes an\nadditional delta-contribution which is necessary for obtaining this result. The\nLienard-Wiechert field and charge-current density must therefore be interpreted\nas nonlinear generalized functions, i.e., not just as distributions, even\nthough only linear operations are necessary to verify charge-current\nconservation. The four-potential from which this field and the conserved\ncharge-current density derive is found to be unique in the sense that it is the\nonly one reducing to an invariant scalar function in the instantaneous rest\nframe of the point-charge that leads to a point-like locally-conserved\ncharge-current density.",
"arxiv_id": "physics/0612232",
"authors": [
"Andre Gsponer"
],
"categories": [
"physics.class-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Derivation of the potential, field, and locally-conserved charge-current density of an arbitrarily moving point-charge",
"url": "https://arxiv.org/abs/physics/0612232"
},
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