# What ACTUALLY causes a magnetic field to be generated when there is a current?

I have asked a few people this question and the most common answer is, "that just seems to be the way nature works." That definitely is not good enough. What is the physical REASON why a magnetic field is generated when a current is running through a wire?

Thanks!
~Matt

Pengwuino
Gold Member
That just seems to be the way nature works.

Teehee. Really though, that's about as good as you'll get. Why does an accelerating charge produce light? Why does mass generate a gravitational field? The best physics can tell you is what mediates or mathematically describe what is going on. At some point you just have to accept something exists.

Doc Al
Mentor
That definitely is not good enough.
That approach limits you to only understanding things that can be explained in terms of things you already know. Doesn't hurt to ask, but often there's new physics to be found that cannot be understood using the old, familiar concepts.

Dale
Mentor
2021 Award
Out of idle curiosity, what sort of answer would be good enough?

dx
Homework Helper
Gold Member
Watch this video:

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Watch this video:

VERY interesting video! Man that is cool stuff. Thanks!

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1. Fantastic discussion, thank you for the question.

2. Fantastic video. That guy... he's smart. And he brings up the natural question: if we don't yet understand why our hand doesn't go through the chair, then we're hopeless to know why there is a magnetic force.

3. As an exercise for (super-) theoretical physicists, I would ask this question:

How many arbitrary force fields could we assign to the universe which would obey the "conservation of energy" as we know it. What I'm saying is, since the electrical, strong/weak, magnetic, and gravitational forces are all "arbitrary" or "axiomatic" (as far as our understanding of them goes), I wonder how many different kinds of force fields there could actually be? Might a different universe have different force fields?

I agree with you Matt. The equation F (magnetism) = qv x B is very curious. The equations for determining the magnetic field B are even more curious. Unfortunately, I don't see how we can ever get past the fact that our understanding of the universe is limited to our perception of it. We didn't come up with those equations on a chalkboard! We came up with them after years of rigorous, painstaking experimentation.

How many arbitrary force fields could we assign to the universe which would obey the "conservation of energy" as we know it. What I'm saying is, since the electrical, strong/weak, magnetic, and gravitational forces are all "arbitrary" or "axiomatic" (as far as our understanding of them goes), I wonder how many different kinds of force fields there could actually be? Might a different universe have different force fields?

I agree with you Matt. The equation F (magnetism) = qv x B is very curious. The equations for determining the magnetic field B are even more curious. Unfortunately, I don't see how we can ever get past the fact that our understanding of the universe is limited to our perception of it. We didn't come up with those equations on a chalkboard! We came up with them after years of rigorous, painstaking experimentation.

To put in complicated terms..
"consider the electron in the lab frame... when it moves you record a current and a mag. field..
on move with the electron's reference... you can see ONLY a time dependent electric field..
all electrons in the current will generate a superimposed field that will..show as a mag field.."
..this is a really confusing answer given by a certain physicist...

the simplest explanation is...THE ELECTRON IS MOVING....since we know electric and magnetic fields are two facets of the same coin..from maxwell's laws..only seen completely in different frames.. it just depends on how you see it..if ur the experimenter..u'll see a force [qv B]...but while moving with the electron you will see a electric field..E(t)..
that's my take on it..

VERY interesting video! Man that is cool stuff. Thanks!

That is a very cool video and Feynman does a great job explaining dealing with the question "why" which science does not ask or answer. And Feynman show the problems in dealing with "why" questions. But you also need to note that Feynman is cheating just a bit because the original questions asked by the interviewer was really more along the lines of "how" does this happen and that is a different question from "why".

If you ask "why is the sky blue?" or "why does a current generate magnetic forces?" An investigation into more and more details forces you further and further back in more "why" questions as Feynman explains in detail, until you are simply left with answers that the sky is blue because God made it that way! And then one has reduced a scientific question to a religious one.

On the other hand if you ask HOW is it that the sky appears blue you have a different question. It is the one that Feynman is avoiding presumably because he doesn't want to say on TV that physics does not have "all the answers". And of course most people know that for light coming through the atmosphere we have a MODEL and by using that model we achieve an ANALOGY between that we do not know and that with which we are familiar. If we say the unknown acts like this other thing we know well, then we feel we have a certain handle on the unknown. And we do. For example, one can use our model to predict results in circumstances that we've never tried in an unknown phenomenon. That is downright practical! We still don't know "why" things act as they do but we do have a handle on "how" they act!

Fine. So now when you ask the question what "actually" causes the magnetic field from a current, you really are asking "why does a current produce magnetic forces about itself?" Can't answer. "Why" questions are off-limits. Well, then, HOW does it do it? Well the usual approach is to flood you with mathematics. And that would be because the "model" that explains the phenomena is a mathematical model. But for you that isn't quite what you mean is it? Because a mathematical model is just an abstract creation with no anchor in reality. What you are asking is to understand the thinking of Maxwell who created the mathematics by using an analogy with the flow of fluids. And his model even invented a fluid to fit the bill they called "aether". And for a time people were satisfied with that as a "how".

But as time went on and more things were measured, it was discovered that while the mathematics still predicts correct answers, the fluid model began to fail and soon it was totally rejected. Thus the problem from your point of view is that at present there simply is NO analogy that one can use for a model to "explain" how a magnetic field works. There are no "fluids" moving from here to there delivering forces or energy. There are no familiar mechanisms that we can recognize and instantly understand how a current delivers a magnetic force at a distance delayed by the speed of light. That model is today simply missing. For that matter we even know the mathematical model is not correct at all scales of measurement.

So what is a "magnetic field"? Well, a field is a mathematical description of vectors over a region of space. In this case it is force vectors. So then a magnetic field is really just the "behavior" of those forces say about a current-carrying wire. But here's the fly in the ointment: Today there is no model to say HOW those forces arise. Therefore physicists make the illogical claim that these fields ARE "behavior"! They call them "behavior fields". Don't forget the forces are real and exist. So how does an object consist of only it's behavior? It's creating something out of nothing. It's illogical. It's as illogical as saying light waves are propagated without any medium. So the bottom line is that with no model, behavior alone is accepted as an "object".

So what you've discovered is that scientists really don't like to stand up in front of the world and say "we really don't have any idea "how" that works. What they'll always say, is: "Here, let me tell all the things we DO know about that, whether relevant to your question or not!"

But don't expect science to hand it all to you on a silver platter. If there's no model that's working for some phenomenon, then it's up to YOU to think about it and try to understand HOW it all could work. Maybe you'll be right. Maybe you'll be wrong. But that is what science is all about.

I wouldn't say it's quite fair to characterize the aether concept of Maxwell and other prominent scientists as being a type of fluid. I think they all very much realized it could not be a fluid as we know them. Nor some type of super-gas which had been mentioned probably more often in those days. But the differential equations describing EM have pretty much the same form as for fluid behavior.

Maxwell and subsequent physicists actually built mechanical models of the aether using cog wheels and belts and such. They obviously didn't confuse them with the actual behavior of the medium but used them as a crutch to form a more concrete idea of the stresses and movement of energy.

Stress is probably the most powerful word to apply to magnetic behavior. Moving a charge causes flow of energy into a region of the medium and therefore causes a stress or build up of potential energy there. Nature urgently wants to remove stress whenever possible (just like us). So apparently she counteracts by venting the energy away from the built up region by forming a counterflow of magnetic energy.

It wouldn't work to have a counterflow in the opposite direction as that would only increase or double the stress in the region that energy has moved from. So nature's only recourse is to create a neutralizing flow at 90 degrees.

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the first two answers gave you quite the best explanation.
the magnetic field was and still is a miracle of nature because it does not exist so often in nature. and the only thing you could explain about it is why on some places there is a field and on others not. the best answer so far, after being considered by great minds as faraday maxwell and who else not is that when charge is not moving there is no mag field and if it does there is. and thats the most natural explanation there will ever be because movement is sort of a structural basis for everything we experience.

By the way Matt, occasionally there is a post or two here encouraging a person to dig deeper and investigate things that have no clique answer. That's really how science works when it is functioning. I think you realize that you do not have to belong to the old gentleman's complacency club. I hope you never settle for less than your perceptive mind tells you it should.

Thanks a lot for the video man !

VERY good and informative answers everyone! This kind of thing is what fascinates me so much in Physics!!

I wouldn't say it's quite fair to characterize the aether concept of Maxwell and other prominent scientists as being a type of fluid. I think they all very much realized it could not be a fluid as we know them. Nor some type of super-gas which had been mentioned probably more often in those days. But the differential equations describing EM have pretty much the same form as for fluid behavior.

Maxwell and subsequent physicists actually built mechanical models of the aether using cog wheels and belts and such. They obviously didn't confuse them with the actual behavior of the medium but used them as a crutch to form a more concrete idea of the stresses and movement of energy.

Certainly not an "ordinary" fluid, but interestingly enough, Maxwell's equations are based upon the model of an incompressible fluid. There are people even today who with some justification say that an electric current should be modeled as a compressible fluid. They point to the effects of ultra high currents on metal conductors as some justification for this view. I'm also guessing that the success of Maxwell's equations pretty much says that a gaseous compressible Aether was not a good choice.

And let me add that Maxwell's mechanical model of an electrical transformer is quite a thing to behold! You'll find it on page 228 volume II of the Dover edition of Maxwell's Treatise on E&M. [Maxwell's section 584] It is an excellent "crutch" or what I'd call a "thinking tool" to help understand the rather strange behavior of transformers. But then "thinking tools" are really what all physical models really are!

Well, in order to explain correctly what is magnetism, you need relativity. Math is a bit hard, but the concept is easy:

Coulomb's law is only valid for electrostatics. When you move a charge, part of the electrical field is "transformed" to magnetic force. It's like the components of a vector when you rotate your referential, part of one component is transformed into another component.

So, in essence, electricity and magnetism aren't as far apart as it sometimes seems to be when you look at the equations.

I might be reading too much into this question, but it seems like the OP was trying to understand the fundamental cause of magnetism. And for the record, to the OP and to everyone else, "that's how nature works" is always a horrible answer because it doesn't tell you anything. You're just stating the obvious. "Magnetism has something to do with the alignment of spin" could have been a better starting point than the dismissive tone the OP encountered...

Cleonis
Gold Member
[...]
What is the physical REASON why a magnetic field is generated when a current is running through a wire?
[...]

As Richard Feynman points out: taking explanation to the next level is possible only if the questioner has mastered the physics that is involved in that deeper level.

It has been shown that special relativity unifies electricity and magnetism: it is possible to describe magnetic force as a relativistic side-effect of the Coulomb force.

Daniel Schroeder has created a webpage with an exposition of http://physics.weber.edu/schroeder/mrr/MRRtalk.html" [Broken].

On that page there is also a link to a 39-page text supplement
http://physics.weber.edu/schroeder/mrr/MRRnotes.pdf" [Broken]

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You can derive the Maxwell equations and the Lorentz force law from only Coulomb's law by demanding Lorentz invariance. So, like some others have suggested here, the answer is Special Relativity.

Well, if you're willing to accept on faith the fact that stationary charges produce electric forces on other stationary, and the principle of relativity, then you can actually prove that moving charges must create another kind of force on other moving charges. We call this the magnetic force. (Yes, I know you may quibble with me about quantum effects like ferromagnetism, but I'm speaking classically.)

Who has asked, are the presumptions of the question in error?

Dale
Mentor
2021 Award
if you're willing to accept on faith the fact that stationary charges produce electric forces on other stationary, and the principle of relativity
Are you being deliberately provocative? You don't need to "accept on faith", there is ample experimental evidence. You belittle both faith and science with such comments.

There is also experimental evidence for magnetic forces. So you must assume one or the other first for the above logic on special relativity to follow. And since you cannot always transform away electric forces, the electric force must be assumed. So, the real question is, what actually causes an electric force.

Are you being deliberately provocative? You don't need to "accept on faith", there is ample experimental evidence. You belittle both faith and science with such comments.
I'm sorry, I think you misunderstood what I was trying to say. Of course there is ample experimental evidence for electrity and relativity, just as there is ample evidence of magnetism. But the OP wanted to know WHY currents produce magnetic fields, not whether they do so or to what extent they do so. So when I told him that his question can be answered if he is "willing to accept on faith" electricity and relativity, I was trying to say that if he was willing to put aside the questions "Why do charges create electric fields?" and "Why is the principle of relativity true?", then his original question could be answered. I wasn't talking about religious faith, but faith in the broader sense of not questioning something.

Dale
Mentor
2021 Award
Sorry, I may be oversensitive to that topic.

Since no one took the bait I offered a few posts up...

There is a different answer than those so far presented.

We may begin by positing a 4-vector field on a smooth spacetime manifold (even one having curvature). We assume it is a continuously differentiable field. The field goes by the name of the 4-vector electromagnetic potential. Various elements of the (manifestly covariant) derivatives of this field are associated with: magnetic fields, charge and current, electric fields, magnetic charge and current which are identically zero by mathematical identity, and other measurable quantities.

A direct result of positing the field alone and making associations with measurable things are: Maxwell's equations, charge continuity, and an infinitude of wave equations and other identities not so common.

There is no cause and effect relationship between these elements such as between current and magnetic fields as assumed in the opening post. By our one simple postulate, the magnetic field and the current are both aspects of the 4-vector field, and must appear together in the experimental arrangement of a conductive, currrent carrying wire in relative isolation.

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But then it would be better to start with a complex scalar field and then demand local U(1) gauge invariance. This then explains why the four-vector fields and tensors exist in the first place.

But then it would be better to start with a complex scalar field and then demand local U(1) gauge invariance. This then explains why the four-vector fields and tensors exist in the first place.

Facinating, and are you sure? I had no idea. Could you explain in more detail, because I don't follow?

Facinating, and are you sure? I had no idea. Could you explain in more detail, because I don't follow?

Consider a complex scalar field described by a Lagrangian density of the form

$$\mathcal{L} = \frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi^{*}-V\left(\left|\phi\right|^{2}\right)$$

where V is some arbitrary potential which can include a mass term.

This is clearly invariant under the global gauge transformation:

$$\phi\rightarrow\phi\exp(i\alpha)$$

You can use Noether's theorem to find what the conserved current is. You can try to make the theory invariant under local gauge transformation, i.e. for alpha that depends on the space time coordinates. If you consider an infinitesimal space time dependent gauge transformation (so we take alpha to be infinitesimal and work to first order in alpha), then apart from total divergences that vanish upon integration, an extra term of the form

$$J^{\mu}\partial_{\mu}\alpha$$

where J is the conserved Noether current, will be generated. You can try to get rid of this by including a term proportional to

$$A_{\mu}J^{\mu}$$
in the Lagrangian where A_{mu} is a new vector field that under gauge transformation is assumed to yield the derivative of alpha so that the extra term you got above, cancels. However, the current itself produces a term under gauge transformations, proportional to:

$$|\phi|^2 \partial^{\mu}\alpha$$

So, the A_{mu}J^{mu} term we included in the Lagrangian will now produce an additional unwanted term proportional to:

$$|\phi|^2 \partial^{\mu}\alpha A_{\mu}$$

This we can get rid of by adding a term proportional to

$$|\phi|^{2}A_{\mu}A^{\mu}$$

in the Lagrangian. We then don't get any additional unwanted terms.

Finally, the vector field A_{mu} can make a contribution to the Lagrangian without a coupling to the scalar field. A gauge invariant contribution can be constructed as follows. The anti-symmetric tensor

$$F_{\mu \nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$$

is clearly invariant under gauge transformations, so we can include a term proportional to

$$F_{\mu \nu}F^{\mu \nu}$$

in the Lagrangian.

Thank you Count Iblis, especially over all the Latex work. I'm been slow in responding, not because I don't appreciate it, but because I've had nothing intelligent to say in response.

Though based in quantum mechanics, you've presented it in a manner that the quantum mechanical origin is so nicely abstracted-away it took some time to see it.

In second interesting, we have two wildly different ways to say that a charge is conserved. Yet they can both talk about the same charge.

First is the Noether charge you are familiar with (and I'm barely familiar with). The second doesn't have a name I am aware of. However, if you asked me, "Why is charge conserved?", I could say, "All exact forms are closed." Roughly, but not too roughly, this is just a statement saying partial derivatives commute. The operator equality being

$$\partial_{\mu} \partial{_\nu} = \partial_{\nu} \partial{_\mu}\ ,$$

so that

$$\partial_{\mu} \partial{_\nu} - \partial_{\nu} \partial{_\mu} = 0$$

For instance, because the electric and magnetic fields can be expressed as derivatives of a vector potential, and because of the particular way charge is expressed as the derivatives of the electric and magnetic fields, all the second partials of A cancel each other out with alternate negative signs. It's a very long bunch of second partials, perhaps four factorial of them, and it wouldn't mean much to you anyway, so I won't Latex it.

Why should two distinctly different methods come to the same conclusion?

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