Electrodynamics, wave equation, velocity of waves

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?

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.

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) ?

Re: Maxwell's equations - is there a bigger picture?

PlanarMetamaterials said:

Maxwell's equations are always satisfied.

Do people's assumptions agree with Maxwell's equations? Not always.

Click to expand...

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.

htg said:

beam of EM waves

Click to expand...

As I understand it, magnetic waves and magnetic forces are a different thing from electromagnetic waves. Electromagnetic waves have to do with photons.

BradtheRad said:

As I understand it, magnetic waves and magnetic forces are a different thing from electromagnetic waves. Electromagnetic waves have to do with photons.

Click to expand...

If you believe in photons, then you should look at the TRUE characteristics of photoelectric effect: it is a resonance phenomenon, it has lower and upper limit of frequency.

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?

BradtheRad said:

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...

Click to expand...

1) Photons do not exist at all. Look at lower and upper limits of frequency for photoelectric effect.
2) I am asking about phase velocity of a magnetically longitudinal, electrically torsional wave in ferrite
characterized by (epsr, mur).

So my radio detects photons from a long distance, and need not be within the circle of the antenna's magnetic influence.

Re: Maxwell's equations - is there a bigger picture?

htg said:

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.

Click to expand...

Could you explain how Gaussian Beam of EM waves violates Gauss's Law?

htg said:

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?

Click to expand...

Can you explain how Ampere's Law leads to that equation? And what is meant by the triangle symbol before B, is it Laplacian operator?