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13th February 2018, 17:49 #1
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Maxwell's equations  is there a bigger picture?
Maxwell's Equations sometimes are satisfied and sometimes are not satisfied. Examples:
1) Gauss' Law can be violated e.g. by a Gaussian beam of EM waves.
2) Ampere's law leads to the equation
grad(div(B))  Δ (B) = mu0*eps0*(d^2 B/dt^2) which is violated and then
the wave equation: Δ(B) = mu0*eps0*(d^2 B/dt^2) is satisfied.
Do you have any idea why?

13th February 2018, 17:49

15th February 2018, 16:32 #2
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Re: Maxwell's equations  is there a bigger picture?
Maxwell's equations are always satisfied.
Do people's assumptions agree with Maxwell's equations? Not always.
2 members found this post helpful.

15th February 2018, 16:32

23rd February 2018, 19:12 #3
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Electrodynamics, wave equation, velocity of waves
1) div(B)=0 and div(E)=0 are true only in magnetostatic and electrostatic situations, otherwise they can be violated (consider a Gaussian beam of EM waves).
2) Maxwell's extension of the Ampere's Law is completely false (Otherwise magnetically longitudinal, electrically torsional waves could not propagate e.g. in a ferrite rod or toroid).
As a result, Wave Equation cannot be derived from true laws of Electrodynamics.
My question:
Is it possible to predict the phase velocity of a magnetically longitudinal, electrically torsional wave in a ferrite characterized by (epsr, mur) ?

23rd February 2018, 19:12

23rd February 2018, 23:53 #4
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Re: Maxwell's equations  is there a bigger picture?
I give clear examples where Maxwell's equations are violated.
Maxwell's equations are supposed to be valid in any situation which can
be encountered in Electrodynamics. There are no hidden assumptions.
So take it into account if you are going to post a reply.

24th February 2018, 07:29 #5
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24th February 2018, 15:47 #6
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24th February 2018, 15:47

25th February 2018, 04:22 #7
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Re: Electrodynamics, wave equation, velocity of waves
No doubt you're correct in some regards, but as I understand it, electromagnetic waves are of a different nature than a magnetic field. We can listen to radio broadcasts because the antenna shoots photons, rather than growing and collapsing a magnetic field. So my radio detects photons from a long distance, and need not be within the circle of the antenna's magnetic influence.
Unlike magnetic waves, radio waves (electromagnetic or EM waves):
* bounce off the ionosphere, can go around the world,
* reflect off buildings and airplanes (multipath),
* are directional when broadcast by a suitable antenna (satellites, microwave towers),
etc.
Magnetic fields show a different kind of behavior, although they have a sort of directionality. I haven't memorized all the equations nor similarities or differences. Perhaps it's easy for people to think they're the same phenomenon because they share the word 'magnetic' in their names?

25th February 2018, 12:32 #8
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Re: Electrodynamics, wave equation, velocity of waves
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