Abstract
We show how dimensional considerations, along with study of properties of invariants of electromagnetic fields, lead to the covariant format of dynamical Maxwell field equations with sources. We complement these four differential equations with another four covariant equations that allow us to relate fields to potentials once a gauge is chosen. We describe the Lorentz covariant gauge condition and obtain a covariant 4-vector format for the electromagnetic (EM) potential. We explore the causal solutions of Maxwell equations for moving charged particles. The explicit form of energy-momentum locked in the fields is derived. We note that the Lorentz force is incomplete as it misses the particle dynamics associated with the magnetic dipole moment that any charged or neutral particle can carry. This clarifies that the empirical form of EM force is not yet fully known.
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.
Charles-Augustin de Coulomb (1736–1806), engineer by training, and physicist by vocation. He developed methods to measure magnetic and electric forces showing before 1791 that the electrostatic forces obey Newton’s inverse-square law.
- 2.
Iwo and Zofia Bialynicki-Birula, “The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism,” J. Phys. A: Math. Theor. 46, 053001 & E 159501 (2013).
- 3.
Paul A.M. Dirac (1902–1984), theoretical physicist contributing at creation of relativistic quantum physics, Nobel Prize in Physics (1933) for ‘Dirac equation,’ i.e. the formulation of the relativistic quantum wave theory of the electron. Dirac made many theoretical and mathematical physics contributions, in the classroom his name is associated most often with the ‘Dirac’ \(\delta\)-function.
- 4.
P.A.M. Dirac, “Quantized Singularities in the Electromagnetic Field,” Proc. Roy. Soc. (London) A 133, 60 (1931).
- 5.
Andre Gsponer “Distributions in spherical coordinates with applications to classical electrodynamics,” Eur. J. Phys. 28, 261 & E:1241 (2007).
- 6.
A. Kholmetskii, O. Missevitch, T. Yarman, “Electric/magnetic dipole in an EM-field: force, torque and energy,” Eur. Phys. J. Plus 129, 215 (2014).
- 7.
V. Bargmann, L. Michel, V.L. Telegdi, “Precession of the polarization of particles moving in a homogeneous EM-field,” Phys. Rev. Lett. 2, 435 (1959).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Rafelski, J. (2017). Variational Principle for EM-Fields. In: Relativity Matters. Springer, Cham. https://doi.org/10.1007/978-3-319-51231-0_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-51231-0_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51230-3
Online ISBN: 978-3-319-51231-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)