Electromagnetic Boundary Problems

4    Radiation by Simple Sources and Structures

In this chapter, we will examine the formulation and solution of electromagnetic radiation problems, in which a given source exists in infinite space and we want to find the resultant field. The results of this chapter will be used in the next two chapters to formulate and solve the problem of scattering from various objects.

4.1    POINT AND LINE SOURCES IN UNBOUNDED SPACE

4.1.1    STATIC POINT CHARGE

Consider the simple example of a static point charge of q coulombs in an unbounded homogeneous medium (Figure 4.1). The charge density of such a point charge can be written as

$\rho \left(\mathbf{r}\right)=q\delta \left(x-x_0\right)\delta \left(y-y_0\right)\delta \left(z-z_0\right)\equiv q\delta \left(\mathbf{r}-{\mathbf{r}}_0\right)$

(4.1)

where r₀ = x₀u_x + y₀u_y + z₀u_z is its location. From (2.13) we have ...