# Question About Magnetic Field's and Refractive index?

#### wes

Joined Aug 24, 2007
242
Ok so this question is a little weird.

So the question is first:
How fast will a magnetic field propagate outwards at.
If you had a EM and a Magnetic field Detector then once the EM is turned, it would take some time for the magnetic field to reach the Detector correct?
Most likely the Magnetic field would propagate no faster then Light Speed.

2ND question:
I know that light slows down in certain material's and this is called the Refractive index of whatever(glass, water etc). But does this apply to a magnetic field as well?
I don't think so because unlike like light, the magnetic field doesn't get absorbed and then re-emited constantly, so i would think it's speed would stay constant.
Is this correct?

and Finally: Is there anyway to slow down the propagation speed of a magnetic field?

Some of you might say a magnetic field is stationary and if not changing then it will not propagate outwards but the field has to propagate outwards at say light-speed even if only turned on and kept on at a constant rate ( Obviously it would become weaker and weaker until barely detectable ) because if it were instantaneous then as soon as I turn on a (let's say huge building sized superconducting EM, lol ) Someone on the moon could detect it instantly, and that's impossible.

by the way the detector in the superconductor and moon example could just be a extremely sensitive electronic compass.

I have been wondering about this question for the longest time and though I sure I am correct it my thinking of how it works, I just want to make sure I am.

Thank's for any Responses
Wes

#### steveb

Joined Jul 3, 2008
2,436
This is a good question that has cropped up in electrostatics, magnetostatics and Newtonian gravity. Before Einstein's field gravitational equations and Maxwell's electromagnetic field equation's, people were confused that the simple force laws implied action at a distance, or effectively infinite speed of the effect.

Field theories show that these effects travel at the speed of light, at least in vacuum. In your magnetic example you need to realize that Maxwell's equations show that any time changing magnetic field also has an electric field. The interaction propagates at the speed of light until steady state is reached. (in theory, steady state is never reached, but to a good approximation it can be effectively static locally)

In a material medium, the speed will be less than light-speed and is inversely proportional to the square root of both permeability and permitivity of the medium.

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#### Ghar

Joined Mar 8, 2010
655
I would think suddenly turning on a magnetic field (like an electromagnet) would be like a step function which of course isn't static at all so you would end up with the time varying components and get a propagating wave until steady state.

Refractive index is a function of both permeability and permittivity while the fields are changed by permeability and permittivity themselves. Most materials have a relative permeability of about 1 (non-magnetic) so pure magnetic field isn't affected as often as electric.
Of course a wave (like light) requires both components so modifying one modifies both.

#### wes

Joined Aug 24, 2007
242
So would this mean

"In a material medium, the speed will be less than light-speed and is inversely proportional to the square root of both permeability and permitivity of the medium."

that a magnetic field would propagate slower in medium like say a iron core or something like that?
if so then why?
is it because since if it is changing it is basically act as light would then.
having a magnetic and electric component to the field.

also steveb, what did you mean exactly

The interaction propagates at the speed of light until steady state is reached. (in theory, steady state is never reached, but to a good approximation it can be effectively static locally)

did you mean the interaction with say another EM or the Measurement tool?
or
did you mean the interaction between the magnetic field and the electric field?

#### steveb

Joined Jul 3, 2008
2,436
also steveb, what did you mean exactly ... "The interaction propagates at the speed of light until steady state is reached. (in theory, steady state is never reached, but to a good approximation it can be effectively static locally) "
Well this assumes that the magnetic field is turned on and then allowed to stop changing at the point of origin. Since the effect propagates at finite speed, the changing can never stop if you consider the entire universe. But, this is just theory bull-crap from a practical point of view. As far as our experiments and practical measurements, we find that the measurements are constant after a certain amount of time. We call this the steady state value.

did you mean the interaction with say another EM or the Measurement tool?
or
did you mean the interaction between the magnetic field and the electric field?
I meant the latter. But don't take the word "interaction" too literally. It is just a way of speaking that is used often. Some people get very picky about whether it is correct to say that electric fields generate magnetic fields and vice versa; or, whether they really interact with each other. Basically, they don't really interact but coexist as components of the electromagnetic field tensor. This is just a fancy way of saying that electric and magnetic fields form one physical entity and they are not independent things.

The basic idea of a field theory is that all effects must be local and no action at a distance is possible. So, for the magnetic field to come into being and then to get from the earth to the moon (to use your example), the field starts out as nothing and then begins at a localized point. This implies a time changing magnetic field which also implies a spatially varying electric field. You can't have one without the other according to Maxwell's equations. This spatially varying electric field also changes in time (because it did not exist a moment ago). The time changing electric field implies a spatially varying magnetic field, and the process propagates out in space in this way. Hence, the fields need to propagate from one point, to the next, to the next etc. This occurs as as an electromagnetic effect according to Maxwell's dynamic field equations. According to these equations, any localized effect will propagate at a finite speed. That speed is related to the permeability and the permitivity of the medium. In vacuum, the speed is the speed of light, often called "c" and this is the maximum speed. Materials can slow the net effects down and this is reflected in the material permitivity and permeability.

#### wes

Joined Aug 24, 2007
242
so now the question is how does the Em field generated differ from a Em field of say a radio wave.

Because i can't take an antenna and then emit a EM field and cause a magnet to feel a force, even if the magnet is really close. if it did then it would only be because the magnetic field generated around the coil?

#### t_n_k

Joined Mar 6, 2009
5,455
Whether this has any relevance to the original question or discussion I'm not sure but there are devices such as fibre optic current transducers that make use of the interaction between light and a magnetic field. e.g. Sagnac interferometer.