Maxwell's Equations Tabulation

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Solutions to James Clerk Maxwell's Equations
(c) Robert Neil Boyd

James Clerk Maxwell
by David Thomson, Quantu Aetherdynamics Institute


  • Gauss' Law
  • Gauss' Law for Magnetism
  • Ampere's law
  • Faraday's law
  • Faraday's law with Maxwell's term
  • and over a dozen other equations of Maxwell's were discarded by Oliver Heavisides[1]


Bulletin of the Bureau of Standards, Volume 5 (Google eBook)

Complex Numbers Move Straight
System of Partial Differential Equations: How to Solve Maxwell's Equations Using Linear Algebra
MIT Lecture 33
Topological considerations - Maxwell's equations
author Denis Auroux, Center for Future Civic Media
published Sept. 10, 2009, recorded December 2007
retreived 11:22, 24 August 2010 (UTC)
Physics with Calculus/Electromagnetism/Maxwell's Equations

Heaviside supported four of Maxwell's twenty[?] equations

Oliver “Heaviside could not understand quaternions. So he dispensed with them. Unfortunately, Heaviside had a large influence on subsequent studies of E/M, which excluded the original quaternionic expressions of Maxwell, and thus excluded a wealth of information regarding the true nature of E/M. The most unfortunate exclusion which resulted was the understanding that charge has a hyperdimensional component of flux. This is expressed in the quaternionic version of the Maxwell equations, but has vanished from Heaviside's truncations of the original equations, as found in common use today.” —Robert Neil Boyd [2]

Source: Thinkering

Michael Faraday revolutionized physics without ever writing an equation.
Published on August 21, 2008
One of Faraday's most far reaching insights, summarized as ‘Faraday's Law', states that a changing magnetic field produces an electrical current -- no mathematics involved. Faraday's law was subsequently mathematized, however, by Faraday's younger colleague, the Scottish physicist James Clerk Maxwell. That formulation is what appears in today's textbooks - as one of Maxwell's equations. Nevertheless, Faraday's physical insight clearly preceded any attempt to translate it into mathematical symbols.



“Today we all commonly accept that Maxwell and Einstein equations are correct ones. But, are they? The Twins’ paradox clearly shows that Einstein's (Albert Einstein, 1879 – 1955) special theory cannot be fully correct and that General theory is valid only until twins do not use boson’s particles in their mutual communications. Beside that, the theory of relativity contains some very convenient generalization that facilitates its derivation but further analysis of the theory leads us directly to the some inconsistence: there is a consequent question whether gravitation distorts space or time? If we apply gravitational red shift to the photon we can derive the same equation for frequency distortion as one obtained by applying formula for time axe distortion by the gravitational field. Einstein equation for the influence of gravitational field to the time also contains the radius although it should not exist there because it is not field parameter at all. This clearly shows that gravitational field is not only variable that has influence on speed of time flow in Einstein’s theory. Regarding the fact that Einstein derivation is quite correct there is a question where was done the mistake?”

Source: Dipl. Ing. Andrija S. Radović

From a discussion page on Scalar Field Theory of Wikipedia

Omission of poynting vector sources the cause?

It is my understanding that Lorentz arbitrarily omitted the Poynting vector energies (outside the circuit) from his interpretations of Maxwell's equations for whatever reasons. When the original 20 Maxell equations got reduced to the 4 standard forms in common use today, this part was left out.

It also stands that all currently accepted theories do not properly account for self-field affects or pre-charged states in the frame of reference.

I see no problem in exploring another theory that fully agrees with the observable data, and most current theory, but has a different mechanism of operation, especially when it has more elegant solutions to problems that current theory can not explain.

To argue out of hand, that one theory is rubbish over another, just because they have different explanations for the same phenomenon, seems petty.

To reuse terminology, with different definitions is necessary, we simply do not have enough words in any language for every theory possess its own set of unique terms.

What makes a theory useful is just that, is it useful?

I know the Earth revolves around the Sun, but the statement "The Sun rises in the East, and sets in the West" is still very useful.

SFT may turn out to be the 'Earth revolving around the Sun type of revelation', and it may still make sense to use older theories when you are 'thinking inside the box'.

See also

A forgotten path to new physics
Doug Sweetser, MIT alumni
  • The Galilean Invariance of Maxwell's Equations
Natural Philosophy Alliance (NPA) streaming video recording
Curt Renshaw, October 2011


  1. R. N. Boyd on Oliver Heavisides, Dr. Robert Neil Boyd (link)
  2. Maxwell's Vacuum, Robert Neil Boyd, Ph.D (