Principles of Electromagnetic Waves and Materials, 2nd Edition

1Electromagnetics of Simple Media*

1.1Introduction

The classical electromagnetic phenomena are consistently described by Maxwell’s equations; these vector (see Appendix 1A) equations in the form of partial differential equations are

(1.1)$$\nabla \times \mathbf{E}\left(r\text{,}t\right)=-\frac{\partial B\left(r\text{,}t\right)}{\partial t},$$

(1.2)$$\nabla \times H\left(r\text{,}t\right)=J\left(r\text{,}t\right)+\frac{\partial D\left(r\text{,}t\right)}{\partial t},$$

(1.3)$$\nabla \cdot D={\mathrm{\rho }}_V,$$

(1.4)$$\nabla \cdot B=0,$$

where, in standard (RMKS) units, E is the electric field intensity (V/m), H the magnetic fieldintensity (A/m), D the electric flux density (C/m²), B the magnetic flux density (Wb/m²), J the volume electric current density (A/m²), and ρ_V the volume electric charge density (C/m³).

In the above equation, J includes the source current J_source.

The continuity equation

(1.5)$$\nabla \cdot J+\frac{\partial {\mathrm{\rho }}_V}{\partial t}=0$$

and the force equation on a point charge q moving ...