ABSTRACT

This chapter reviews some of the needed vector analysis for the derivation of the three-dimensional wave equation from Clerk Maxwell’s equations. It explains the basic vector operations; define the gradient, curl, and divergence, and introduce standard vector identities that are often seen in physics courses. This chapter aims to derive the three-dimensional wave equation for electromagnetic waves. This derivation was first carried out by James Maxwell in 1860. The chapter also aims to derive the wave equation for electromagnetic waves. It considers the case of free space in which there are no free charges or currents and the waves propagate in a vacuum. The wave equations lead to many of the properties of the electric and magnetic fields. The chapter analyses systems in which these waves are confined, such as waveguides.