Page 58 - Maxwell House

38 Chapter 1

they generate a stream of positive or negative charges those are decelerated and thus emit the
EM radiation transferring their kinetic energy to the energy of EM fields.

a) b)

Figure 1.7.1 EM field generators: a) Hand-cranked generator, b) MHD generator
To illustrate this conversion process let assume that the flow of positive charges accelerated to
the speed v by some outside mechanical, chemical, heat, gravitation, solar or any other force
are injected between two parallel plates as shown in Figure 1.7.2a.

a) b)

Figure 1.7.2 a) Positive charges are repelled and decelerated, b) Scalar product ∘ < 0

Since these positive charges move in the direction of the positively charged plate, they are
decelerated by the repelling Coulomb force and lose their kinetic energy through radiation.
created by moving charges
Therefore, the equivalent volume electrical current density
provides the excitation of electromagnetic fields. Consequently, the charges transfer their
kinetic energy to electromagnetic fields if the vector of electric field has the component that
decelerates moving charges and the dot product ∘ < 0 (see Figure 1.7.2b). Since the
charge conservation law cannot be broken in any natural process, the continuity equation similar
to (1.36) should occur for the source charges

= 0 (1.76)
∘ +

Here is the volume charge density created by source.
What is not obvious is how to estimate . In general, the time and space distribution of such

source currents is postulated by introducing the source electric current density as independent
value of the electromagnetic fields produced by them. This is not quite right, but we have no
real choices. The main problem is that the behavior of such current sources is not completely
govern by Maxwell’s equations and therefore cannot be found as their solution. Even though
on a present level of numerical analysis and computer science, growing computer power and
availability, it is quite visible to combine several embedded tools in one computation block.
Each of these tools can be based on sophisticated mathematical model in electromagnetic,