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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 field of a moving charge

The field of a moving charge

(p.341) 17 The field of a moving charge
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter begins the study of electromagnetic radiation by calculating the field created by a single moving charge, first when in uniform motion, and then when it is accelerated. It reveals the potential created by a charge in uniform motion starting from the Coulomb expression for the potential in the frame where it is at rest, and then by making a Lorentz transformation. The chapter then follows the exact reasoning for any type of motion by introducing inertial frames tangent to the charge world line. In this way, it obtains the retarded Liénard–Wiechert potential created by a charge in any type of motion. After studying some special cases of the field of a moving charge, the chapter defines the asymptotic, radiation, part of the field.

Keywords:   electromagnetic radiation, moving charge, uniform motion, accelerated motion, Coulomb expression, Lorentz transformation, inertial frames, Liénard–Wiechert potential, radiation field

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