# Fields—Maxwell’s Equations

# Fields—Maxwell’s Equations

Chapter 3 explores the concept of the field, which is necessary to describe forces without resorting to action at a distance, and uses it to describe electromagnetism, as encapsulated by the Maxwell equations. First, scalar fields and the Klein–Gordon equation are discussed. Vector calculus is introduced. The physical meaning of Maxwell’s equations is explained. The equations are then solved for electrostatic fields. Non-uniform charge distributions and dipole moments are discussed. The vector and scalar potentials are introduced. Electromagnetic wave solutions of Maxwell’s equations are found and the Hertz experiment is described. Magnetostatics is discussed briefly. The Lorentz force is described and used to determine the motion of a charged particle in a cyclotron or synchrotron. The action principle for electromagnetism is described. The energy and momentum carried by the electromagnetic field are calculated. The reaction of a charged particle to its own electromagnetic field is considered.

*Keywords:*
Maxwell’s equations, electromagnetic field, vector calculus, electrostatic field, magnetostatics, action principle, cyclotron, synchrotron

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 .