Abstract
The empirical basis of electrodynamics is defined by Faraday’s law of induction, by Gauss’ law, by the law of Biot and Savart and by the Lorentz force and the principle of universal conservation of electric charge. These laws can be tested – confirmed or falsified – in realistic experiments. The integral form of the laws deals with physical objects that are one-dimensional, two-dimensional, or three-dimensional, that is to say, objects such as linear wires, conducting loops, spatial charge distributions, etc. Thus, the integral form depends, to some extent, on the concrete experimental set-up. To unravel the relationships between seemingly different phenomena, one must switch from the integral form of the empirically tested laws to a set of local equations which are compatible with the former. This reduction to local phenomena frees the laws from any specific laboratory arrangement and yields what we call Maxwell’s equations proper. These local equations describe an extremely wide range of electromagnetic phenomena.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In anticipation of subsequent results, we make use of the fact that in time-independent situations, the electric field has a vanishing curl. This is not true in the general case!
- 2.
After L.V. Lorenz who should not be confused with H.A. Lorentz, see Historical Remarks.
- 3.
The closed surface \(F\) may be localized. However, with suitable care it may be continued entirely or partially to infinity.
- 4.
- 5.
As the contribution from the source and the dependence on the test point factorize completely, we have suppressed the prime on the integration variable \({x}^{\prime}\).
- 6.
The derivation given here follows essentially R.A. Sorensen, Am. J. Phys. 35 (1967) 1078. Another, rather natural, approach which does not exhibit the singularity of the contact term derives from the relativistic treatment of hyperfine structure by means of the Dirac equation. It yields the nonrelativistic contact term in the approximation \({v}/{c}\ll 1\). Both aspects are worked out in J. Hüfner, F. Scheck, and C.S. Wu, Muon Physics I, Chap. 3.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Scheck, F. (2012). Maxwell’s Equations. In: Classical Field Theory. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27985-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-27985-0_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27984-3
Online ISBN: 978-3-642-27985-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)