curl

SELF	8
S.B. Karavashkin and O.N. Karavashkina

5. Application of the curl theorem to EM dynamical fields Proceeding from the fact that in EM fields the regularities of general dynamic fields remain their validity, expression (25) for electric and magnetic fields can be written as follows:
	(28)
Comparing the obtained expressions (28) with known Maxwell equations (7), we see them essentially differing. In (7) the time variation of electric and magnetic fields induces relatively magnetic and electric fields. But (28) speaks only that the time variation of electric and magnetic fields causes these vectors circulation appearance, proportional to the velocity of this variation and vectors inclination to the wave propagation direction. This distinction, though essential, does not cause the contradictions between these systems of equations. We can show it easy, substituting the related equations of these systems. Thus, doing so with the second equations, we yield
	(29)
or
	(30)
which corresponds to the conventional relationship between the vectors of dynamical electric and magnetic fields. Similarly, substituting the first equations of these systems, we yield
	(31)
or
	(32)
Substituting (32) into (29), we yield for the transversal vector
	(33)
is reduced the same. Thus we see that, using the conventional relationship (30) between and , we can yield one system from another, and vice versa. Noting the proved theorem of curl of vector and theorem of divergence proved in [10] also for dynamical fields, the complete system of equations describing the EM field takes the following form:
	(34)
In (34) each pair of equations is responsible for its projection of vectors and . The curl of vector for the longitudinal component and the divergence of vector for the transversal component vanish.