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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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Interacting charges I

Interacting charges I

(p.367) 20 Interacting charges I
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter addresses the problem of radiation by a system of point charges. Owing to the fact that the electromagnetic interaction propagates at finite speed, this problem can only be solved iteratively, by assuming that all speeds are small compared to the speed of light. The chapter then derives the dipole and quadrupole formulas giving the radiation field and the energy radiated by the system in the lowest orders. Finding the field and the radiation of a system of charges beyond the dipole approximation is rather more difficult, but necessary in the absence of dipole radiation. This is also a useful exercise for studying the radiation of a mass system in theories of gravitation where the gravitational mass is equal to the inertial mass. In addition, the chapter finds the equations of motion of the charges of the system to third order in the velocities.

Keywords:   interacting charges, radiation, point charges, electromagnetic interaction, dipole and quadrupole formulas, radiation field, equations of motion, velocities

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