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Chapter 2:
Maxwell's Equations and Plane Wave Solutions
Abstract

2.1 Introduction

All electromagnetic phenomena can be said to follow from Maxwell's equations. In Section 2.2, we will write these equations and the constitutive relations and derive the 3D wave equation in a dielectric. In Section 2.3, we will show that plane waves satisfy Maxwell's equations, and will study the properties of plane waves. Finally, in Section 2.4, we will give a physical interpretation of the Poynting vector.

2.2 Maxwell's Equations and the Wave Equation in an Isotropic Dielectric

Maxwell's equations are based on experimental observations and are given by the following equations:

(2.1)

(2.2)

(2.3)

and

(2.4)

where ρ represents the charge density, J the current density, and E, D, B, and H represent the electric field, electric displacement, magnetic induction, and magnetic field, respectively. The preceding equations can be solved only if the constitutive relations that relate D to E, B to H, and J to E are known.

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CHAPTER 2
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