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ECE Equations of Electrodynamics for Electrical Engineering


These can be used as in the Maxwell Heaviside field theory, but with the addition of the spin connection, allowing the possibility of spin connection resonance. In the simplest instance they are:

The Gauss Law

                                                     del B = 0

The Faraday Law of Induction   

                                    curl E + partial B / partial t = 0 

The Coulomb Law

                                                del E = rho / eps0

The Ampere Maxwell Law

                           curl B - (1/ c squared) partial E / partial t = mu0 J 

The difference to Maxwell Heaviside (MH) is that these laws are now written in a space-time with curvature and torsion. They are mathematically the same. In MH however they are written in Minkowski (or flat) spacetime which has no curvature and no torsion. The charge density rho and current density J can be calculated now from line elements in general relativity, and these are now equations of a generally covariant unified field theory, not of nineteenth century classical electrodynamics. The spin connection enters through the relation between the fields and potential. The magnetic flux density is:

                                                  B = curl A - omega x A

(in MH this is B = curl A), and

and the electric field strength is

                          E = - partial A / partial t - c grad phi - c omega0 A + c phi omega

(in MH this is E = - partial A / partial t - c grad phi)

Here omega0 is the timelike part of the spin connection, and omega is the vector part of the spin connection. The spin connection makes all the difference, because spin connection resonance may occur (e.g. paper 63 of , resulting in resonant amplification of voltage from spacetime. These are the simplest type of ECE equations of e/m, they can also be written in the complex circular basis to define the B(3) spin field:

                                            B(3)* = - i g A(1) x A(2)

from a choice of spin connection. These equations can now be used in electrical engineering for any given device.

Civil List Scientist
Posted: 2007-10-22


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