ABSTRACT
Maxwell was able to explain all available experimental facts related to electromagnetism on the basis of equations known collectively as Maxwell’s equations. These equations allows to find the electric and magnetic fields at each point of space at any moment of time. An important property of Maxwell’s equations is that they are invariant under the Lorentz transformations. This means that the equations have the same form in all inertial coordinate systems. This chapter briefly discusses Maxwell’s equations and applies those to several simple problems. Maxwell’s first equation expresses Gauss’s law for the electric field. Maxwell’s second equation is the generalized Ampere’s law. Maxwell’s third equation shows that not only the electric charges but also time-varying magnetic fields can be the source of an electric field. Maxwell’s fourth equation is Gauss’s law for the magnetic field. The chapter also includes exercise problems related to electromagnetic fields.
