Page 46 - Maxwell House

26 Chapter 1

1.6.9 Why Do We Need Extra D-Vector Describing E-Fields?

According to the ancient philosopher Aristotle, “Nature abhors a vacuum.” “Obeying” Aristotle
the world around us is full of matter in different states/phases: solid, liquid, and gases. Under
the special conditions, the matter may be in a state of plasma, superconductivity, and some
exotic for engineering practice states like quantum, Bose-Einstein condensate, super fluid and
solid, supercritical liquid, etc. The reader can find further information in the specialized
literature. We will focus on conventional materials widely used in everyday life and devoted
Chapter 2 to the neoclassical theory of interaction of EM fields with dielectrics, metals, ferrites,
etc.
Why do EM fields interact with matter in the first place? By the classical atomic model, the
-4
9
basic units of matter are minute atoms whose estimated nucleus diameter is in order of 10
Å. Meanwhile, the average atom diameter is in the order of several ångströms. Roughly
speaking, there is a lot of “free space” inside and outside atoms that gives the primary EM fields
a good chance to penetrate and encounter with the nucleus positively charged protons as well
with the negatively charged electrons. Lorentz’s force “obliges” these fields to transfer some
portion of their energy to the charged particles. The latter start oscillating about a point of
equilibrium, i.e. moving back and forth around their stationary positions, or just shifting slightly
in case of static fields. If we assume that a neutron has a mass of 1, then the relative mass of an
3
electron is minute and 0.00054386734 only. It means that each electron in almost 2⋅10 times
lighter than a neutron and thus might have a much higher oscillation magnitude. Thereby any
charge movement is equivalent to some electrical current. Consequently, each such moving
charge (most electron) has to induce the secondary EM fields that are added to the primary.
Therefore, the total E-fields inside the matter might strongly diverge from the primary in the
vacuum. To take into consideration this effect we can adjust the constitutive relation (1.27) as
= where the dimensionless coefficient called the relative dielectric constant of
0

matter. Thereby, we include all additional fields induced by matter bound charges into D-vector
and maintain the flux of D-vector defined by (1.26) dependable on the free electrical charges
only regardless of the E-fields induced inside the matter by these free charges. It is important

to observe that free charges are those not bound up in atoms and molecules of the matters.
Meanwhile, the charges on the surface of conductors (see Section 2.2.7 in Chapter 2) induced
under influence of the external E-fields must be considered as free charges.

1.6.10 Electric Charge Conservation Law in Differential Form

Before settling (1.32) into Maxwell’s House let us formulate the continuity equation for electric
charges. In particular, this equation is one of the possible forms of the electric charge
conservation law that can be expressed as any decrease in the amount of charge in a given
region of space must be correctly balanced by a simultaneous increase in the quantity of charge
in an adjacent region of space. Since any charge, give-or-take a few, means the flow of moving
electric charges or the electric current the describing such movement equation

-10
9 1 Å = 10 m