Introduction to Mathematical Physics/Electromagnetism/Introduction

At previous chapter, equations that govern dynamics of a particle in a field of forces where presented. In this chapter we introduce electromagnetic forces. Electromagnetic interaction is described by the mean of electromagnetic field, which is solution of so-called Maxwell equations. But as Maxwell equations take into account positions of sources (charges and currents), we have typically coupled dynamics--field equations problem: fields act on charged particles and charge particles act on fields. A first way to solve this problem is to study the static case. A second way is to assume that particles able to move have a negligible effect on the electromagnetic field distribution (assumed to be created by some "big" static sources). The last way is to tackle directly the coupled equations system (this is the usual way to treat plasma problems, see exercise exoplasmapert and reference ([#References|references])). This chapter presents Maxwell equations as well as their applications to optics. Duality between representation by forces and by powers of electromagnetic interaction is also shown.