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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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The Lorentz force

The Lorentz force

Chapter:
(p.281) 11 The Lorentz force
Source:
Relativity in Modern Physics
Author(s):

Nathalie Deruelle

Jean-Philippe Uzan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198786399.003.0029

This chapter studies Maxwell theory by defining the electromagnetic potential and field as well as the force exerted by an external field on a particle carrying an electric charge. In Maxwell theory, the fundamental mathematical quantity representing electromagnetic phenomena is a field of covariant vectors (or a field of 1-forms), the electromagnetic potential, with components Aμ‎(Xν‎) in a given inertial frame with Minkowski coordinates Xν‎. A quantity derived from the potential plays a central role because it is this quantity rather than the potential itself which directly represents observable phenomena. In addition, this chapter integrates the equation of motion for the cases of uniform rectilinear and circular motion. It follows the four-dimensional approach, which, being more efficient and transparent, can also give the main results in 3-vector notation.

Keywords:   Maxwell theory, Lorentz force, electromagnetic potential, electromagnetic field, electromagnetic phenomena, Lorentz rotation, electric charge

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