Abstract
As second basic application of the general solution (6.64) of Maxwell’s equations we determine the electromagnetic field generated by a particle following a generic strictly time-like trajectory, see condition (7.3). This field plays a fundamental role in classical electrodynamics and is named after its discoverers, A.-M. Liénard (1898) (L’Éclair. Électr. 16:5, 53, 106, 1898, [1]) and E.J. Wiechert (1900) (Ann. der Phys. 309:667, 1901, [2]). The solution of Maxwell’s equations for light-like trajectories, not achievable with the Green function method, will be addressed in Chap. 17.
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Notes
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- 2.
At the quantum level this means that we consider as emitted only those photons which are able to reach spatial infinity, without being reabsorbed by the charged particles.
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Actually, it can be shown that the acceleration and velocity fields both satisfy the Bianchi identity exactly: \(\partial _{[\mu }F_{a\,\nu \rho ]}=0=\partial _{[\mu }F_{v\,\nu \rho ]}\).
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References
A.-M. Liénard, Champ électrique et magnétique produit par une charge électrique concentrée en un point et animée d’un mouvement quelconque. L’Éclair. Électr. 16, 5, 53, 106 (1898)
E.J. Wiechert, Elektrodynamische Elementargesetze. Ann. der Phys. 309, 667 (1901)
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Lechner, K. (2018). Liénard-Wiechert Fields. In: Classical Electrodynamics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-91809-9_7
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DOI: https://doi.org/10.1007/978-3-319-91809-9_7
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