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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 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.
- 3.
Actually, it can be shown that the acceleration and velocity fields both satisfy the Bianchi identity exactly: \(\partial _{[\mu }F_{a\,\nu \rho ]}=0=\partial _{[\mu }F_{v\,\nu \rho ]}\).
- 4.
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-91809-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91808-2
Online ISBN: 978-3-319-91809-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)