# Current producing electromagnetic force

1. Jun 29, 2007

### kgm2s-2

When current is allowed to flow through an electric conductor, magnetic fields are produced. What actually causes the magnetic fields to appear?
:rofl:

2. Jun 29, 2007

### Staff: Mentor

What sort of explanation are you looking for, that is, what do you mean by "actually causes"?

3. Jun 30, 2007

### kgm2s-2

It means that when current is flowing through a straight wire, how is magnetic field created around that wire? That is, what happens in the wire which causes this phenomenon to occur?
And why does the magnetic field change direction (from clockwise to anticlockwise or vice versa) when the current is flowing in the opposite way,
according to the Maxwell's screw rule or right-hand grip rule?

4. Jun 30, 2007

### WMGoBuffs

The superficial answer to your question is just "Maxwell's Equations," but I think what you're asking is much deeper, akin to "What actually <i>is</i> a magnetic field?" That's tougher to answer.

5. Jun 30, 2007

### cabraham

That's a very good question. Unfortunately, neither I, nor anyone has ever found an answer. The "cause and effect" concept is intuitive at the macroscopic level. If you tee up a golf ball, then swing the club, hitting the ball and putting it into flight, it is intuitive that the kinetic energy of the club was partially transferred to the ball, "causing" it to move.

At the microscopic level, though, what causes what is usually unknown. It is impossible to define everything, since definitions would be circular. What causes the magnetic field has not yet been detected. If we ever do discover a smaller more basic particle, then the question becomes "what causes its behavior".

Some properties are basic and cannot be proven or derived from something else. When a wire carries a current, years of empirical observation have demonstrated the existence of a magnetic force, and no exceptions have ever been found. We postulate this, i.e. no formal proof is given. We don't really know what causes magnetism. Maxwell's equations quantify this property and are postulates. Maxwell's are basic and are not derived.

Likewise with electric fields, voltage, current, and Coulomb force. Why two like charges repel one another is unknown. We've observed that they do, and no one knows the "cause".

"Cause and effect" is difficult to distinguish when you're dealing with basic particles and their associated interactions. What "causes" gravity is along those same lines, i.e. it is postulated that two masses attract each other mutually from empirical observation. No one knows the cause. I hope this helps. Best regards.

Claude

6. Jun 30, 2007

### ice109

lots of philosophical mumbo jumbo but no real substance. there are theorized answers to this question, just because you don't know them ( and coicdentally i don't know them ) doesn't mean you need to resort to saying that it is absolutely unknown.

"The modern understanding of magnetism posits that all magnetic effects are actually due to relativistic effects[4] caused by relative motion between the observer and the charged particles."

7. Jun 30, 2007

### waht

Magnetic field is just a relativistic effect of the electric field. When the charge is not moving, it has an electric field, and no magnetic field. However when it moves close to the speed or light, the electric field lines will be compressed, and a sort of tidal force will develop, which is the magnetic field. The strength of the magnetic field depends on how fast the charges move.

$$B = v * E/c^2$$

(cross product)

Last edited: Jun 30, 2007
8. Jun 30, 2007

### cabraham

No offense ice109, but you are the one not making sense. If no one, neither you, nor I, nor anyone, knows the answer, then it is indeed *unknown*. When I say "unknown", I don't infer that it will never be known, nor do I infer that it doesn't exist. Unknown simply means just that, i.e. magnetic force can be sensed and measured but we don't have the answer as to what causes it. So it really is unknown. I'm not "resorting" to anything other than stating what centuries of science have and have not revealed.

As far as relative motion between the charged particle and observer goes, isn't that by definition what *current* is?! If charges are moving with respect to my reference frame, the charge per unit time is what is known as current, i.e. 1 amp = 1 coulomb / second. So what you're saying is that the magnetic field is due to *current*. But we already know that, don't we?! The OP asked us what causes the magnetic field around a current-carrying wire, and your answer is that the current causes it. Very well. This is what I mean by "circular definitions". Peace.

Claude

9. Jul 1, 2007

### jostpuur

In my opinion this matter is highly mystical in main stream science. I can hear everybody explaining, that putting electricity and relativity together will give magnetism, but I have never seen actual proof for this claim. Some years ago, being not satisfied by these "rumours" about magnetism, I tried to deal with this problem myself.

Two facts before getting into business:

1: Somebody might say that you cannot use action at the distance in relativity. Nonsense! Just make sure that the action at the distance has proper time delay. Suppose partice A is in location $$(0,\boldsymbol{0})$$ in spacetime, and particle B in location $$(|r|/c, \boldsymbol{r})$$, then sure we can solve what force A is exerting on particle B.

2: You are not supposed to use forces in relativity. Nonsense! Just define $$\boldsymbol{F}:=d\boldsymbol{p}/dt$$. It is a good definition, and nobody has right to forbid this concept.

Now consider a following problem. A particle A is moving with velocity $$\boldsymbol{v}_A$$, and a particle B is moving with velocity $$\boldsymbol{v}_B$$, and we want to know what force particle A exerts on particle B. Let us assume that the locations in the spacetime are like in the earlier remark, so that the question makes sense.

I understood, that there is no need to postulate this answer. In particular there is no need to postulate magnetic field or Lorentz's force. It is sufficent to postulate Coulomb's force in the A particle's rest frame. Since we can calculate how four-position and the force itself transforms under boosts, we should be able to solve the force in any other frame. Unfortunately I cannot put in all the details, because the calculation is quite long, but I hope you understood the idea. So we postulate the force B feels is $$\boldsymbol{F}=\lambda \boldsymbol{r}/|r|^3$$, in the frame where A is rest, and solve what this force is in the original frame where particles have the given velocities. After lot of work the result is this

$$\boldsymbol{F}=\frac{\lambda(1-|v_A|^2/c^2)}{(|r|-\boldsymbol{r}\cdot\boldsymbol{v}_A/c)^3} \Big(\boldsymbol{r} - |r|\boldsymbol{v}_A\frac{1}{c} +\boldsymbol{v}_B\times(\boldsymbol{v}_A\times\boldsymbol{r}) \frac{1}{c^2}\Big)$$

Now it could be useful to divide this expression into particle A depending part, and particle B depending part, and it can be done with following definitions.

$$\boldsymbol{E}:= \frac{(1-|v_A|^2/c^2)}{(|r|-\boldsymbol{r}\cdot\boldsymbol{v}_A/c)^3} \Big(\boldsymbol{r} - |r|\boldsymbol{v}_A\frac{1}{c}\Big)$$

$$\boldsymbol{B}:= \frac{(1-|v_A|^2/c^2)}{(|r|-\boldsymbol{r}\cdot\boldsymbol{v}_A/c)^3} (\boldsymbol{v}_A\times\boldsymbol{r})\frac{1}{c^2}$$

With these definition the force is the given by the usual Lorentz force $$\boldsymbol{F}=\lambda (\boldsymbol{E}+\boldsymbol{v}_B\times\boldsymbol{B})$$. (Okey the constants aren't standard in these equations, but it's not important)

For some time I though I had all magnetism now figured out, but I later learned that these equations agree with the Maxwell's electromagnetism only in the special case where particle A is not accelerating, because the radiation terms are missing. And the original assumtion on the Coulomb's force is also wrong for accelerating source. Still, I would argue that these were not useless calculations, because they give good intuition on the nature of magnetism. In my opinion, the popular calculations that deal with lorentz contractions of current carrying wires are too special case like, to truly answer problems of magnetism and relativity.

If we now accept the fact that we don't need to worry about radiation yet, and are merely interested in the forces (as students in the early steps are), I can give a very specific answer to the question why and what magnetic field is. It is an artificial concept, invented by man, to make calculations easier and to divide the force expression into parts that depend on the source and the test particle separately. Ultimately, the force has its origin in Coulomb's force and Lorentz's transformations. So the question "what is magnetic field" is reduced to questions "what is Coulomb's force" and "what are Lorentz's transformations". That is a big step.

The more succesfull field point of view doesn't fully agree with this, and I sure don't want to fight against fields. But it is always good to know lot of different ways to deal with these phenomena, isn't it?

Last edited: Jul 1, 2007
10. Jul 1, 2007

### jostpuur

What I meant with those comments about the topic being mystical, is that even though I've got quite far on my own, I still don't know how to get nicely full electromagnetism with radiation, by somehow "putting electricity and relativity together".

For example I've read how Ohanian & Ruffini derive ED in their relativity book, and it's like "let us postulate nice differential equations". Well I guess it looks good if you have lived your whole life with field differential equations, and consider that approach trivially the only possibility, but I'm still sceptical about its rigourness.

The fact that many phycisists seem to think that the force is somehow old fashioned concept, that doesn't belong to relativity, also sets under question, that do these people know anything on this matter.

Last edited: Jul 1, 2007
11. Jul 1, 2007

### jostpuur

kgm2s-2, I was just taking part in the discussion, I don't know if my post helped you in any way. At what level are you? How much you know about physics?

12. Jul 1, 2007

### ice109

what i meant is that i haven't learned the physics yet. there is physics that explains b field. it is not unknown at all. i'm pretty sure quantum field theory explain the electromagnetic force but like i said i don't know it.

13. Jul 4, 2007

### stmartin

In the atom, the protons and electrons are neutralized so that means that there is no charge=no electric force=no electric field. It is like moving neutral ball produces magnetic field.

14. Jul 4, 2007

### pervect

Staff Emeritus
The situation is hardly "mystical" but there are some subtle and not-so-subtle points here.

Can you give an example of someone saying that you cannot use "action at a distance", for instance retarded potentials? I have a feeling of a strawman being scattered all over the floor here.

Again, can you give an example of someone saying you can't use forces in special relativity?

On a separate note, there are other ways of handling forces in special relativity, i.e. 4-forces - using forces rather than 4-forces is not guaranteed to be the best choice.

Here is the first subtle point. You also have to postulate that in A's reference frame, the force on B is independent of B's velocity. This is true for electromagnetism, but is not true for some other "forces", i.e. gravity for instance.

I haven't looked at this closely, but I believe that this is a perfectly standard calculation that one can find in textbooks, see for instance

http://en.wikipedia.org/w/index.php?title=Electromagnetic_four-potential&oldid=136870056

This has the general name of Lienard-Wiechart potentials. This is usually expressed in terms of a 4-potential, rather than a force. The force is just the gradient of the 4-potential, so it's fairly trivial to go from the force -> potential.

I don't think the calculations were useless either, but it seems to me that a certain amount of re-inventing the wheel has occurred.

The way I would describe the situation would be this:

A coulomb force (more preciesely, the 4-force equivalent) alone, is not Lorentz invariant - it doesn't transform in the way that a force must according to relativity. The 4-force must transform just as any other 4-vector - and this defines how the 3-force must transform.

The combination of electric + magnetic forces together, is Loretnz invariant, therefore we call the force the "electromagnetic force" in relativity, just as we refer to "spacetime" in relativity rather than space+time. The electric and magnetic forces are two parts of the same entity.

However, in spite of the fact that the electric and magnetic forces are two parts of the same force, it is not quite true that one can deduce the precise form of the magnetic force from the electrostatic force (Coulomb's law). One has to make additional assumptions about the force on a moving charge.

Last edited: Jul 4, 2007
15. Jul 6, 2007

### stmartin

Why you thing that the electric field lines (electric force) will be compressed?

16. Jul 6, 2007

### kgm2s-2

Nevertheless, thanks for your contribution. I'm in O-level physics if you're wondering.

17. Jul 6, 2007

### stmartin

So, let's conclude. Why does moving electron produces magnetic field?

18. Jul 6, 2007

### Staff: Mentor

19. Jul 6, 2007

### stmartin

There is nothing concretely said there. I just wanna know, correctly how it is. I saw on some posts that said that the electric field is compressing and producing tidal force, which is the magnetic force. Can you explain better please. Thank you.

20. Jul 7, 2007