Jump to ContentJump to Main Navigation
Solved Problems in Classical ElectromagnetismAnalytical and Numerical Solutions with Comments$
Users without a subscription are not able to see the full content.

J. Pierrus

Print publication date: 2018

Print ISBN-13: 9780198821915

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198821915.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 07 July 2020

The electromagnetic potentials

The electromagnetic potentials

Chapter:
(p.373) 8 The electromagnetic potentials
Source:
Solved Problems in Classical Electromagnetism
Author(s):

J. Pierrus

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198821915.003.0008

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .