Speed of a longitudinal magnetic wave in ferrite

If I wind a short coil on a ferrite rod and run AC through it, then a wave will go through the ferrite rod. This wave is magnetically longitudinal and electrically torsional. My question is: is the speed of such a wave equal to c/SQRT(εr*μr) ?

Probably not. There's no thing like a "magnetic wave", I presume. An electromagnetic wave can theoretically propagate in ferrite medium, practically it won't for longer distance due to huge ε and μ loss angle. What you see in the setup is a magnetic near field. My guess is that it's not affected by εr.

Why do you think the speed of an EM wave in ferrite will not be affected by εr?
I think it should be affected by εr and by μr.

The speed of an electromagnetic wave would be affected. But you don't observe an electromagnetic wave in the described situation, just a reactive near field.

An electric field (constant) has no magnetic field associated with it. Similarly, a constant magnetic field has no electric field associated with that.

Now consider a variable (sinusoidal wave) electric field: it is always associated with a magnetic field and effectively it is electromagnetic wave. Same is true for a variable magnetic field.

A part of the energy is radiated from the coil (it is an antenna is some sense) - it is lost forever.

Yes, you have electromagnetic radiation that can be plane polarised or circularly polarised or anything in between. But it is not possible to have a wave that is magnetically longitudinal and electrically torsional.

Perhaps I have not understood the question.

Imagine a short coil wound on a long ferrite rod. Clearly if you run AC through the coil, you will get magnetic wave along
the rod. It will be accompanied by a torsional electric wave. You can have a transformer in which you have this situation.
Because of the torsional electric wave I think εr as well as μr should affect the speed of the wave.

1. Forget about the ferrite rod for the time being; we shall take care about that later...

2. Consider a single turn coil for simplicity; this is a condition that can be easily modified...

3. Consider an AC source connected to the two ends (close by) of the turn of the coil.

4. The electric field is in the plane of the coil and is parallel to the radius (there is no electric field within the conductor).

5. The magnetic field is perpendicular to the turn- (in the direction of the ferrite rod)

6. In this particular case, the plane of the electric field and the plane of the magnetic field is indeterminate- the radiation from the coil is unpolarized- the rod radiates EM perpendicular to the ferrite rod (axis of the solenoid) in all direction.

7. I presume by 'torsional' you imply what we call circularly polarized; the electric wave is NOT circularly polarized in the present case.

8. To give a simpler example: consider a unit charge hanging from a pendulum that is moving with a period of 1Hz. Because the charge is moving, the current is also moving (sinusoidal motion) - the EM wave will be plane polarized in this case.

But anyway, the magnetic or electric fields travel at the speed of light in that medium. Hence you are correct to say the velocity of the wave will be dependent on epsilon and mu.

Point 4. requires a correction: electric field is in the plane of the coil and goes in circles e.g. concentric with the turn of the coil.

By "torsional" I do not mean "circularly polarized". I mean that the direction of the E field is along the circumference of the rod
- this E field is caused by time-varying longitudinal magnetic fied.

Clearly the time-varying magnetic field has to be accompanied by a torsional electric wave - this is why transfomers work.
On the other hand there is the question: has anyone solved Maxwell equations without assuming div(E)=0 and div(B)=0 ?
- I guess this can be important for near-field.

More clearly, a charge moving in a circular path with const speed can be decomposed into two orthogonal simple harmonic motions (sine waves) but with a phase diff of 90 (one is a sine and the other is a cosine wave).

So you end up with two electric fields, both in the same plane (plane of the coil), perpendicular to each other, and both vary sinusoidally.

The phase diff between the two is 90 but that still leaves out the phase of the first one. This lack of information gives rise to unpolarized (some call it uniformly polarised)- different from circularly polarised - light (EM radiation). If you can somehow fix the phase of one, you will get circularly polarised radiation.



A sinusoidally varying magnetic field (say in the XZ plane) gives rise to a sinusoidally varying electric field (in the YZ plane).

to understand how transformers work, it is best to consider two parallel conductors separated by a small distance.

If the varying magnetic field is in the Z direction, it gives rise to torsional electric field going in circles in XY plane.

Electromagnetic waves are all transverse in nature; if the varying magnetic field is along the Z axis, the direction of the propagation will be perpendicular to the Z axis (say X axis)

The electric field will then be perpendicular to the XZ plane, that is Y axis.

You need to consider the direction of the electric field at a given point as a function of time. It is certainly possible to have different direction of the electric field at different points.

It is not possible to have electric field vector (or magnetic field for that matter) along the same direction as the direction of propagation (why?)

My example clearly shows that an EM wave can be magnetically longitudinal and electrically torsional.

It's a magnetic field with associated with an associated electrical field, not a distinct wave.

I give up. But there are many good text books on electromagnetic theory.

Yes, it is near-field. It is not clear to me what its speed is going to be.
By the way, has anyone solved Maxwell's equations without assuming div(E)=0 and div(B)=0?
I think these assumptions are violated in near-field.

Consider a magnetically longitudinal near-field wave in a ferrite rod.
Maxwell's equations lead to grad(div(B)) - ΔB = - μ*ε*(d^2 B/dt^2).
This is not non-trivially satisfied e.g. by B(x,y,z,t) = B0*cos(k*z-ω*t), where B0 is a vector in the Z-direction, because then
we get grad(div(B)) = ΔB.
What expressions for B are solutions describing magnetically longitudinal (near field) waves?