# What is a magnetic field? (fun mental exercise)

1. May 7, 2015

### meBigGuy

Think of a charged particle moving parallel to a wire carrying a constant current. The magnetic field caused by the constant current exerts a force on the moving particle (say it moves towards the wire).

Now, think of the same thing from a different reference plane. Think of a still particle near a parallel moving wire (same distances, charges, current, and relative velocities). In other words, shift from the reference plane of the wire at rest to the reference plane of the particle at rest.

The particle must be affected by the current in the same way. It must move toward the wire. So, how does that happen? Where does that force come from?

It's an interesting problem, and leads to the conclusion that a magnetic field in one reference plane is an electric field in the other, brought about by relativistic motion. In reality they are the same thing.

COOL

http://www.feynmanlectures.caltech.edu/II_13.html Section 13.6

2. May 8, 2015

### Staff: Mentor

Bingo, you got it. In different inertial reference frames, electric becomes magnetic, and magnetic becomes electric.. The are actually the same thing, called electromagnetic fields.

3. May 8, 2015

### Baluncore

You cannot have magnetic fields without electric fields. They are quite dependent on each other.

Consider a length of link chain made of a conductive magnetic material. Pass a wire carrying AC current through the end link.
That will create a magnetic flux in the end link which will then induce an electric current in the next link. The process repeats along the chain in alternate links.

At the far end of the chain you hang a detector on a small loop of wire.
Depending on whether there is an odd or even number of links in the chain, the detector may or may not detect the input signal.

The detector response is now independent of the number of links, every link has both a magnetic flux and an electric current flowing.

4. May 9, 2015

### meBigGuy

Your example is about electric currents (I) and magnetic fields (B), not electric fields (E).
The point is that electric fields and magnetic fields are not different things, but rather, different views of electromagnetic fields.

To a stationary electron, a moving wire, conducting current, appears positively charged.
(There is a relativistic change in charge density relative to the stationary electron caused by the moving wire.)
To a moving electron, the magnetic field produced by a current in a wire causes it to arc toward the wire.

"magnetism and electricity are not independent things—that they should always be taken together as one complete electromagnetic field. Although in the static case Maxwell’s equations separate into two distinct pairs, one pair for electricity and one pair for magnetism, with no apparent connection between the two fields, nevertheless, in nature itself there is a very intimate relationship between them that arises from the principle of relativity."

and

"We have found that we get the same physical result whether we analyze the motion of a particle moving along a wire in a coordinate system at rest with respect to the wire, or in a system at rest with respect to the particle. In the first instance, the force was purely “magnetic,” in the second, it was purely “electric.”

I was unaware of the role relativity plays in the character of electromagnetic fields.

It's also interesting that the introduction of relativity didn't change Maxwell's equations.

5. May 9, 2015

### jim hardy

hmm

i'm hung on the thought the moving wire must carry its magnetic field along with it. So the QV cross B term in Lorentz doesn't change - you said relative velocities are the same.

I wont say any more until i make it through that Feynman lecture.

6. May 9, 2015

7. May 9, 2015

### Staff: Mentor

Jim,

Visualize yourself riding on a train with a trapped charge in a balloon. Are you electric or magnetic? You on the train has a different answer than you on the platform.

Learn it best from the master teacher Leonard Susskind

8. May 9, 2015

### Baluncore

But you cannot be in two different places at one time, so it must appear as magnetic or electric depending on where you really are and what it really is. That does not make it both at the same time to you. Sitting on the fence is not an option here.
When you toss a fair coin it comes down, (static), heads or tails, (electric or magnetic?). But if you rest or spin the coin on it's edge, how it appears will depend on your viewpoint.

9. May 10, 2015

### meBigGuy

whether it APPEARS magnetic or APPEARS electric, it is electromagnetic. Of course it can also APPEAR as a combination of both magnetic and electric. it just depends on your frame of reference. You say it depends on "what it really is", as if it is "really" electric or "really" magnetic. What it is is "really" electromagnetic.

10. May 10, 2015

### Staff: Mentor

Where analogies fail, resort to the math. Stedwards posted the true answer, the Farsday Tensor. I also posted the video lecture that will teach you about the Faraday Tensor.

11. May 10, 2015

### meBigGuy

"The electromagnetic tensor is completely isomorphic to the electric and magnetic fields, though the electric and magnetic fields change with the choice of the reference frame, while the electromagnetic tensor does not."

The thing about the 4 Maxwell equations is that their conditions are such that the reference plane is fixed.

"This tensor simplifies and reduces Maxwell's equations as four vector calculus equations into two tensor field equations."

Regarding what Jim said about the magnetic field "moving" with the wire. That's an obvious and intuitive way to consider it, but I wonder how the moving wire would affect a compass? Is there actually a moving magnetic field? Can a magnetic field "move" in that sense (along an infinite wire moving along the axis of current flow)?
After all, the electron's displacement is such that a moving magnetic field would describe it exactly.

BTW, this is all new to me and I am not a mathematician. I'm not a fields guy either.

12. May 10, 2015

### stedwards

The fields don't move, by definition. Amplitudes can decrease in some places, and increase in others. An electromagnetic wave is an example.

Spacetime is four dimensional. So one has to wonder why electromagnetism, as commonly expressed, has these 3 dimensional vectors E=(Ex, Ey, Ez) and B=(Bx, By, Bz). You can think of these two 3 dimensional vectors as the space-like and time-like parts of the same thing. Like this: E=(Ext, Eyt, Ezt) and B=(Bxy, Byz, Bzx). These are the elements of the Faraday tensor.

But there is a simple 4 dimensional vector associated with electromagnetism. It's called the 4-vector potential, A=(At, Ax, Ay, Az). The component At is the familiar electric potential phi, expressed in volts. The remainding three are called the magnetic potential.

The electric field is due to the change in electric potential over a distance, combined with the change in the magnetic potential over time. Ex = d(Ax)/dt + d(At)/dx. For Bx, it's like a cross product. Bx = d(Ax)/dy - d(Ay)/dx.

We're dealing with 4 dimensions instead of three. A reference frame in motion with respect to another reference frame is comparable to one coordinate system rotated with respect to another in 3 dimensional space. It's called a "boost". During any rotation or boost the length of the vector A doesn't change, but the values of the components do. This is why an electric field in one frame of reference can look like both an electric and magnetic field in another reference frame; the components of A are different, as well as the components of spacetime.

Last edited: May 10, 2015
13. May 11, 2015

### jim hardy

i found a printable copy of that Feynman magnetostatics page.

Will be back. Dont want you folks to think i'm not interested .

Faraday Tensors look really fearsome. I dont have the vocabulary to handle the link you posted.

And this
is counter-intuitive to me. A magnetic field must accompany whatever is producing it - else marine compasses wouldn't have compensating magnets.

Thanks, guys

14. May 11, 2015

### Jony130

15. May 11, 2015

### stedwards

By example of fields that don't move, there are surface waves on water. The wave itself propagates, but the water itself is relatively fix (a particle of water driven by a series of waves moves in small circles). The question never seems to come up in engineering setting where either concept seems to work just as well as the other.

A magnet itself seems to carry it's field with it, but if it's in relative motion it would have an accompanying electric field.

Taken to it's conclusion, the field of electric charge density doesn't move either, but most people would hesitate to adopt this point of view, insisting that charge moves, or something similar. This goes for electric current density as well.

16. May 11, 2015

### meBigGuy

Again, think of an infinite wire carrying a current. It has a magnetic field radiating out from the wire that attenuates with distance. But, there is nothing to distinguish the field along the axis of the wire at a given distance. It is of fixed intensity, the same all along the wire. If the field is moving, what is it that is moving? If a put a wire (not carrying a current) perpendicular or parallel to the moving wire, what would it detect? It would see a fixed magnetic field. I don't think it can tell the wire is moving.

17. May 12, 2015

### Staff: Mentor

Yes but also think of the looped magnetic lines we see at the surface of the sun. They are made visible by the plasmas they carry. Those lines move and grow and shrink as we watch. Isn't that a moving field?

18. May 12, 2015

### Baluncore

Is it the path taken by the current through the plasma that is moving and so dragging the magnetic field with it? Or is it the magnetic field that is driving the plasma? MHD says it is both. Every current is intimately looped by a magnetic field and every magnetic field is intimately looped by a current.

You cannot have E without M in our finite impedance Universe.

19. May 12, 2015

### meBigGuy

I can't really comment on the specifics of plasma flows on the sun, but I didn't say (or mean to imply) that fields, in any general sense, don't move.
If you move the wire laterally, the magnetic field strength in space changes. That would be a "moving magnetic field". If you move it along the axis of the current carrying wire, there is no magnetic field strength change laterally from the wire or anywhere in space, so how can you tell the wire is moving by the magnetic field? (but when it is moving along the axis of current flow it displays an electric charge)

Last edited: May 12, 2015
20. May 13, 2015

### stedwards

Fields don't move.

There are no associated velocities in Maxwell's equations. In the Lorentz force equation, the velocity is associated with electric charge.

Last edited: May 13, 2015