Benj wrote:

On Jul 16, 10:18 pm, Andrew Usher wrote:

Charge, after all, is quantised, and the derivatives therefore are all
either zero or infinite. Therefore the differential equations can only
be an approximation, while the integral forms are exact. This can also
be checked by noting that the integral form can be proven from the
differential (divergence theorem etc.), while going the other way
requires an assumption of continuity.

1. Maxwell's equations are based upon an incompressible fluid model.

No, they are not.

Thus, they fail when functions are not continuous and differentiable.

This sentence proves beyond the shadow of a doubt that you have never taken
- much less passed - a course in electrodynamics.

This is easily shown for example in that switching circuits do not
follow Faraday's law of magnetic induction.

Oh, do we have a retired engineer on our hands?


2. Both the differential and integral forms fail at quantized (non-
continuous) levels.

That's because classical E&M is ... get this ... classical. However, the
covariant Maxwell's equations work just fine for quantum field theory.


3. Any continuous fluid model will require enough discrete elements so
that they approximate a continuous fluid to some degree or it fails to
give even approximate valid answers.

Maxwell's equations aren't based on fluids. Moron.


4. Math is not more real than reality.

Since you understand neither, I suppose we should take your word for it.


5. I hope you've noticed that everyone attempting to "answer" your
question is a moron.

Have you ever set foot inside a classroom that taught the subject?

Have you ever read a book that taught the subject at a level commensurate
with your mouth? Griffiths? Jackson? Hmm?