Electromagnetic Theory; Maxwell's Equations; Ivor Catt

Heaviside versus Rolling

Ivor Catt 30 December 2008

Heaviside versus Rolling

"The Catt Question" has exposed a fundamental weakness in the grasp of electromagnetic theory by professors and text book writers. This was perhaps not so serious before 1960, when electronics gravitated towards digital electronics and the Transverse Electromagnetic Wave (TEM Wave) came to the fore. This is because a signal from one logic gate to the next in high speed logic has to be seen as not instantaneous, but travelling at the speed of light, guided by the two conductors - signal line and 0v return line. The word "return" illustrates the problem. The signal, or current, does not "return", but travels at the speed of light in the dielectric guided by the two conductors. The idea of "return" is fallacious. All travels forwards.

The transition from steady state fields and slowly varying fields, such as those leading to Faraday's Law of Induction, were not properly developed in the first instance towards the TEM Wave. Manipulation of the four Maxwell Equations, as written by Heaviside, resulting in the TEM Wave was faulty.

The fact that since 1965, in the new pre-eminence of high speed logic, it was no longer acceptable to accept the idea of instantaneous action at a distance, for Instance Faraday's Law of Induction v = d(phi)/dt ; that the voltage developed round a loop equals the rate of change of magnetic flux through the loop, was no longer true since in the new situation change of magnetic flux through the far end of a loop was "elsewhere" to the point of measurement, and could not affect it instantaneously, as Faraday's Law wrongly implied.

Buried beneath the confusion was the "discovery" by Faraday that changing magnetic field caused electric voltage and thence current. This "discovery" reinforced the "Rolling Wave" version of the TEM Wave. In fact, we now see that magnetic field does not cause electric field, and electric field does not cause magnetic field. Rather, they are co-existent. Further, any apparently isolated electric field, or any apparently isolated magnetic field, is really the sum of two superposed electromagnetic fields, both containing both electric and magnetic field (at right angles to each other) travelling in opposite directions at the speed of light.

Now two of Maxwell's Equations are;

dE/dx = - dB/dt (1) and

dH/dx = - dD/dt (2)

These equations give mathematical credibility to the idea that if one field is changing, on the right hand side, it causes the other field. However, the equation which was never published until 1985 is

dE/dx = - (constant) x dE/dt (3)

This equation presents the idea that changing field E causes field E! In the previous two equations, use of two symbols for E and two symbols for H conceals a constant, similar to the constant in (3), making them structurally the same as (1) and (2). We have to conclude that, to the extent that the changing electric field causes the electric field, which is absurd, so the implications of (1) and (2), that changing electric and magnetic fields cause each other, are equally absurd.

In (1), 2) and (3), the relevant constants are a combination of the permeability and permittivity of space. They are of course the link between E and D, and B and H, explaining why (1) and (2) appear to have no constants.