Page 39 - Maxwell House

BASIC EQUATIONS OF MACROSCOPIC ELECTRODYNAMICS 19

Integral Form Differential Form Comments

7 = = Constitutive relation

8 = = Constitutive relation
0
0
Maxwell’s equations tell how the electromagnetic fields arise from such sources as charges and
currents, which are nothing more than moving charges. Electric and magnetic fields are deeply
interconnected, any variation in any of them leads to a proportional change in another one. They
can be independent/decoupled if they are produced by the sources independent of time, as
shown in Figure 1.5.1b, where Maxwell’s House cuts down to façade and back wall only.
In Maxwell’s House, any shift from level up or down is the
movement in space and, as expected, the div operator ( ∘), curl-
operator ( x), or vectorial rotation ( x) provides such upstairs
or downstairs alteration. Any displacement on the same floor level
is the time domain movement in parallel to the vector that exerts
this movement.

Now we can start building Maxwell’s House step-by-step. First,
let us put Lorentz’s force in the top left node of the first floor as
shown in Figure 1.5.2. Since the vector, E is connected with
vector through the scalar operation, it must be located on the
same level while the vector B connected through the vectorial
Figure 1.5.2 operation must be put one level down. For a while, we stop
Vectors , E, D, H populating Maxwell’s House in order to define the vectors E and
and B in Maxwell’s B.
House
Note that each component of the electric or magnetic field, charge,
current, and matter parameter (if they are not defined differently) in Table 1.7 is the function of
time t and coordinates (x,y,z). It is convenient to use the vector notation for coordinates =
+ + . There and then we assume in Table 1.7 and following text that =
0
0
0
(, ), = (, ), = (, ), = (, ), and so on.

1.6 ELECTRIC AND MAGNETIC FIELD VECTORS
1.6.1 Vector of Electric Field Strength

The Encyclopedia Britannica defines the electric field as “ … an electrical property associated
with each point in space when the charge is present in any form. The magnitude and direction
of the electric field are expressed by the value of E, called
electric field strength or electric field intensity or simply
the electric field. Knowledge of the value of the electric
field at a point, without any explicit knowledge of what
produced the field, is all that is needed…” to know. What
else can be said about the electric field, which is pretty
hard to visualize except in narrow optical window?
Practically nothing about its nature but we can detect and

Figure 1.6.1 Integration path count it using the monopole sensor #1 carrying tiny
charge. According to Lorentz’s equation (1.11) the small