# The origin of magnetic fields

1. Apr 11, 2007

### Rainbow

Can someone please explain in details the origin of magnetic fields. I mean, how do electric fields produce magnetic fields and how do magnetic fields produce electric fields and all the other details.

2. Apr 11, 2007

### Crosson

Imagine you see current going down a wire. The wire is electrically neutral, the total charge is zero (negative charges are moving, lets say, to the left, but the stationary positive charges cancel their electric field). Pretend you don't know about magnetism, and so you say "the force from the wire is zero because the net charge is zero and the electric field is zero".

Now, electrons in a wire move very slowly, so in theory I could run along side the wire you see, myself exactly matching the drift speed of the electrons which constitute the current you observe, but going in the opposite direction that they are drifting.

What do I see? Remember I am moving at constant velocity so that my frame of reference is inertial, and so I have as much right to consider myself at rest as do you. Thus, I see a positive current moving past me, and a negative current moving past me at twice the speed.

Now, due to special relativistic length contraction, I will see more electrons/meter then I do protons/meter, and so I will feel an electric force!

But special relativity forbids there to be a force in one inertial reference frame without it being in another, and so there must be a force in your frame as well. We can derive the force in your frame by doing a lorentz transformation from my frame of reference to yours, and after this transformation the equations look different, so we call it a different force: magnetism.

In general, a pure electric or pure magnetic field will look like a mixture of electric and magnetic fields in any other inertial frame of reference.

3. Apr 11, 2007

### ShawnD

Crosson, that's some interesting stuff, but it doesn't seem to explain (in simple terms) why magnetic fields are perpendicular to electric fields. If the fields/forces are to cancel each other out, shouldn't the magnetic field be parallel to the electric field, but moving in the opposite direction?

4. Apr 12, 2007

### Mentz114

1. Electric fields do not produce magnetic fields - electric currents, i.e. charges in motion produce magnetic fields.
2. Magnetic fields do not produce electric fields - charges produce electric fields.

What about EM radiation ? Well you don't need charges or currents in EM radiation so I can't say how the E and M fields are sustained in EM waves.

Perhaps someone could enlighten us ?

5. Apr 12, 2007

### cesiumfrog

That may be the case for EM waves, but no such thing is true in general.

Firstly, you do need an oscillating charge or current to produce constant EM radiation.

Perhaps it's easiest to understand if you consider only the E- part of the radiation. Consider a charge moving up and down, and slow it right down for simplicity: when the charge is up the top you would expect the electric field everywhere to point at it, and when the charge is somewhere else the electric field would be slightly different so as to still point toward the charge. (Similarly for just the -M part of the field, if the source was instead a slowly oscillating current in a coil.)

When you speed up the oscillation however, you'll find the field doesn't change "instantaneously" at great distances because of special relativity again: information can't propagate faster than light (so the distant field doesn't know how to point where the electric charge is "now" yet), so instead the changes propagate at speed c, producing a wave in the electric field.

Then, if you understood all that Crosson was saying, you could in principle go through the math to investigate the changing electric field from different points of view, and deduce the magnetic field from the relativistic effects..

6. Apr 12, 2007

### Staff: Mentor

Static electric fields do not produce magnetic fields. Changing electric fields do produce magnetic fields. This is described by the $\partial \vec E / \partial t$ term in Ampere's Law.

Static magnetic fields do not produce electric fields. Changing magnetic fields do produce electric fields. This is described by Faraday's law of Induction.

The combination of these two effects allows electromagnetic waves to continue to propagate through space, even after their source (a radio transmitter or light bulb or whatever) "turns off."

7. Apr 13, 2007

### rbj

8. Apr 17, 2007

### Ahmed Abdullah

We know that moving charge produces magnetic field and when charge is accelerated it gives rise to EM wave.

Now Let a unit charge flow at constant velocity, say to the positive x axis. We will have a changing electric and magnetic field at any given point, say it is the origin. The change in electric and magnetic field has no periodic relationship with time, actually both m and e fields are decreasing with time. At these circumstances can we expect any EM wave?
The charge is not accelerating so the possible answer is NO. Besides there is not periodicity in the change, so if there to be a wave it should have infinite frequency.
As cesiumfrog has stated information cannot travel at infinite velocity.
Now the question is that how this change of electric and magnetic field travels?
I suppose it is ......I have no idea

9. Apr 17, 2007

### Mentz114

Apparently it's Ampere and Faraday effects which move it along. Join the club, nobody knows.

10. Apr 17, 2007

### rbj

that's not accurate that nobody knows. it's the solution of the partial diff eqs you get from Ampere's and Faraday's Law (or two of the Maxwell's Eqs.). why these laws are true? that's axiomatic in Classical physics. considering special relativity, all you need for axioms are the first of Maxwell's Eqs. (equivalent to Coulomb Law) and SR and the other effects are derived.

11. Apr 17, 2007

### Mentz114

rbj, I think I meant 'nobody knows exactly how or why..'.

The fact that the laws are axiomatic, ie not derived from something else, or arise from relativity enforces my point (?)

Anyhow, I still find it wonderful and mysterious, pace Faraday, Ampere, Maxwell, Coulomb and the rest.