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Solved Problems in Classical ElectromagnetismAnalytical and Numerical Solutions with Comments$
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J. Pierrus

Print publication date: 2018

Print ISBN-13: 9780198821915

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198821915.001.0001

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The electromagnetic potentials

The electromagnetic potentials

(p.373) 8 The electromagnetic potentials
Solved Problems in Classical Electromagnetism

J. Pierrus

Oxford University Press

This chapter expresses the fields E(r, t) and B(r, t) in terms of the electromagnetic potentials Ф(r, t) and A(r, t), and shows that these potentials are defined only up to a gauge transformation. This leads the reader naturally to the Coulomb and Lorenz gauges which are usually encountered in textbooks. The inhomogeneous wave equations whose solutions are the retarded electromagnetic potentials are also considered, as well as the Lienard–Wiechert potentials for an arbitrarily moving point charge. A few questions are included in which the Lagrangian and Hamiltonian of a point charge are expressed in terms of Ф and A. The chapter concludes by deriving a multipole expansion for the dynamic vector potential which will provide the starting point in our treatment of electromagnetic radiation later on in Chapter 11

Keywords:   scalar potential vector potential, gauge transformation gauge invariance, gauge function Coulomb gauge, Lorenz gauge in homogeneous wave equation, retarded potential Lienard–Wiechert potential

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