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Re: Tesla Coil RF Transmitter

Original poster: stork <stork@xxxxxxxxxxxxxxxxxxx>

Hello Antonio,

You introduced "displacement current" when you argued Maxwell's equation:
curl H= J+dD/dt
This equation does not fit or apply to the experiment at hand of waving a macroscopic chaged body back and forth longitudinally. Maxwell's equation curl H= J+dD/dt requires an electrically closed loop circuit. 

 From where comes this requirement? A straight wire, ideally infinite,
has a perfectly measurable magnetic field around it.
A moving charged body too, because everywhere around it, dD/dt is nonzero.
Antonio Carlos M. de Queiroz


I'm very glad you ask this question.

First I'll address your examples. An infinite straight wire is physically impractical as well as impossible. If it were possible to stretch a straight wire to infinity there would be no magnetic field around it per se. To have a magnetic field around the wire would require an electric current in the wire. The current would require a source and drain. This source/drain would constitute an element in the electrically closed loop circuit. So, too, a moving charged body in a conductor (such as an electron) creates a current and subsequent magnetic field around the conductor. I agree with you. An electromotive force is required to move the charged body. Again, the EMF is associated with a power source and drain which is part of the electrically closed loop circuit. The equation most applicable is I = dq/dt for current in the wire conductor.

The electrically closed loop requirement comes from Ampere's law which was a simplification of the Biot-Savart law. Maxwell "borrowed" Ampere's law and expanded on it by adding his displacement current. Amperes law uses line integration which requires a closed path of integration, sometimes called an Ampere loop. Ampere's law states that the integral of B.dl around any closed path is muoI, where I is the current crossing any surface bounded by the path of integration.

Ampere's law and its requirements exist unchanged in Maxwell's curl H= J+dD/dt. So, if you have a conductor with a current and magnetic field then the loop requirement is not only implied, but required to satisfy Maxwell's and Ampere's equations.

If a capacitor is added to the electrically closed loop then Maxwell's, curl H= J+dD/dt, equation applies in its entirety for time varying currents. There is still line integration of an electrically closed loop though.

Electric fields don't require line integration of a closed loop. Gauss's law (also "borrowed" by Maxwell) with area integration applies.

The whole thrust of my proposed experiment and this thread is to revive the concept of electrodynamics. That all things electric do not have to pass through the myopic portal of electromagnetic theory. There is a much older and richer theory of electrostatics and electrodynamics. Unfortunately these are theory(s) that modern practitioners and EE schools have done their very best to ignore or completely squelch.

Stork

Incidently, I'll be giving a presentation on the mechanism of action of asymmetric capacitor thrusters (lifters) this weekend at the grand daddy of all Teslathons, TCBOR in Richmond. I'll touch briefly on the myth of "displacement currents" and why they never display magnetic fields which are the EM sine qua non of electric conduction currents. Hopefully I will see some of you there.