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## How does movement of an electric charge create a magnetic field?

I've been researching this for hours and yet cant seem to get an understanding.

So, let's take an electron fixed in space. At any given time it has an electrostatic field around it which decreases with distance and uses photons as a force carrier. It has an elementary charge e- and will attract protons/repel electrons.

Now let's say you have 2 electrons within each other's electrostatic fields, however we are "holding" them so that although they are experiencing repulsive forces, they are not moving.

Now let's say i take one electron and start moving it.
This means that relative to each other, both are moving.

This means that immediately, both start to invoke a magnetic field on each other, correct?

question 1: But what does this even mean? The only difference i see is that electron 1 will still be applying an electrostatic force but the strength of that force will vary from stronger to weaker as i move the electron closer or farther from the other electron.

Question 2: I dont even understand the functional difference of a magnetic field. This is the magnetic field that can attract certain metals, and can repel or attract ends of a magnet, right? Does it do anything else?

Question 3: But isnt that just the same as having a negative or positive net charge in a substance based on a local abundance of protons or electrons? And an object wouldnt have to be moving to exert a net electrostatic force and repel or attract something. So how on earth does MOTION of electrons create a magnetic field?

Question 4: For emphasis of 3: What's so special/necessary about the "motion" aspect in creating magnetic fields?

Question 5: Where on earth does this magnetic field come from? I dont understand what in the system changes that you get this fundamentally new (yet interconnected) force. The force carrier is still the photon, and the electrons still have an elementary charge, but now the location of that charge point is changing, so the only outcome i can see is that an affected body would be increasingly or decreasingly subjected to the strength of that charge point as it moves over time... I have no idea where the magnetic aspect comes in..

If someone could clarify my misunderstandings and gaps in knowledge it would really make my day!

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Welcome to PF.

This means that immediately, both start to invoke a magnetic field on each other, correct?
No, it does not work that way. When you shake the first charge, the standard view is that the magnetic field is generated in the charge and starts spreading out to space with the speed of light in every direction. Technically, the field is called to be "retarded", since the field at some distance will be function of past motion of the charge.

Only the first charge has non-zero field, the second charge, being at rest, keeps its electrostatic field.

The magnetic field is present in the sense that moving charges would experience magnetic force. However, as the magnetic force acts only on moving charges, there is no action of magnetic field on the second charge. This means that in the situation as you described it, the magnetic field does no exhibit itself.

However, as the first charge was shaken, besides magnetic field, also electric field experiences change and this will affect the force acting on the second charge.

Where the magnetic field comes from? Based on theory and experience, we picture the electromagnetic fields everywhere and connected to the particles. It is difficult to find deeper explanation for their existence.

Do not try to understand this in terms of some light particles - although the idea is attractive at first, you will find that it is very hard to make it work for every aspect of EM field. It is much better, in your position as a beginner, to try to understand electromagnetic phenomena with classical theory of electromagnetism.

Thanks for the answers! I understand a little bit better now, although i still have many things im curious about.

Quote by Jano L. 					 				 				The magnetic field is present in the sense that moving charges would experience magnetic force.
So what exactly does it mean to "experience this magnetic force"? Im not sure what these forces actually do to the charges that pass through them. Does the magnetic field create some kind of attraction or repulsion? How does this attraction or repulsion vary from electrostatic? I read something about 2 electrons travelling side by side- ultimately their electrostatic forces will repel each other, but the faster they go, the magnetic fields they generate will create a higher degree of attraction between the two? I dont understand the mechanism of how this attraction is created via movement, and what exactly it attracts or repels.

However, as the magnetic force acts only on moving charges, there is no action of magnetic field on the second charge. This means that in the situation as you described it, the magnetic field does no exhibit itself.
Ohhh, ok, so not only does the particle have to move to generate a magnetic field, but another particle has to be "moving" through the field to be affected by it.

But in this case how is movement defined? If you have 2 electrons, and one is moving east @ 100 feet per second, and the second is moving east @ 50 feet/sec, they would both exert a magnetic field on each other, correct? But isnt movement relative? Couldnt one say that relative to electron 1, electron 2 is standing still, and electron 1 is going 50 fps?

Sorry for all the questions, my mind just naturally seeks out the root answers and explanations to things...

## How does movement of an electric charge create a magnetic field?

To experience magnetic force means that the particle is under action of force that is perpendicular to its velocity. The exact formula for the force is

\mathbf F_m = q\mathbf v \times \mathbf B

where ##q,\mathbf v## are the charge and velocity vector of the particle and ##\mathbf B## the magnetic field vector.

Here is how you can see the effect of magnetic force on electrons with your own eyes: take magnet and approach old TV or CRT monitor screen. Normally, the picture is formed by myriads of electrons flying from the hot cathode and falling on the screen. When you put magnet on the screen you will see that the colors get distorted by the magnet. The explanation is that the motion of the electrons and the magnetization of the screen is affected by the magnetic field of the magnet and hence they do not fall onto screen as intended for good picture.

In cyclotron, electrons move in horizontal circle thanks to constant vertical magnetic field ; magnetic force constantly curves the trajectory of the particle into a circle.

But isnt movement relative? Couldnt one say that relative to electron 1, electron 2 is standing still, and electron 1 is going 50 fps?
Yes, it depends on the frame of reference. So does the magnetic and electric field.

If you had two charges moving along with the same velocities, from your point of view, they would be surrounded by magnetic fields, but from their point of view, there is just electrostatic field and no magnetic field.

Electric and magnetic field are just two parts of description of interaction between bodies. "How much" of the interaction is described by electric force and how much by magnetic force depends on the frame of reference.

Mentor
[I took too long to write this, and Jano slipped in before me.]

Quote by mpatryluk 					 				 				But isnt movement relative?
Yes indeed! And so is the distinction between electric and magnetic fields.

Consider two stationary charges, one above the other from your point of view as you stand in front of them, and separated by some distance. Each charge produces (only) an electric field, which exerts an electric force on the other charge. If the charges are free to move, they move towards or away from each other depending on whether they are "like" or "unlike" charges.

Now imagine running past the two charges. From your new point of view, the charges are both in motion. In addition to the electric fields and forces, each charge now produces a magnetic field which exerts a magnetic force on the other charge.

Clearly the net effect of the electric and magnetic forces in the second case must be the "same" as the effect of the electric forces in the first case, in terms of the motion of the charges, after taking into account the the difference in your own motion. After all, the charges don't "know" whether you're standing still or running.

We say nowadays that electric and magnetic fields and forces are merely different aspects of a single unified electromagnetic field and electromagnetic force. If we know the electric and magnetic fields in one reference frame (e.g. the one you use when you're standing still), and the relative velocity of another reference frame (e.g. the one you use when you're running), we ought to be able to calculate the fields in the second frame. That is, we ought to be able to transform the fields from one frame to the other.

The question of how to do this in a way that is consistent with how the laws of mechanics transform between reference frames, was a major theoretical puzzle in the late 1800s, which led ultimately to Einstein's Special Theory of Relativity.

Great, everything is starting to make a bit more sense now. I think what threw me off the most was that the electrostatic field is so simple, with such a standard explanation as being the direct result of charge exuded from an elementary particle, so i kind of assumed i should be able to grasp the magnetic component in the same way. However it seems that the explanation for "why magnetic field" has underpinnings in quantum electrodynamics. I was expecting some direct cause and effect explanation, like: when an electron is moving, x, y and z happens with the photon and the electrostatic waves, and BOOM, there's your reason for magnetic fields. I see now that it's much more complicated.

Quote by Jano L. 					 				 				To experience magnetic force means that the particle is under action of force that is perpendicular to its velocity. The exact formula for the force is  $$\mathbf F_m = q\mathbf v \times \mathbf B$$  where ##q,\mathbf v## are the charge and velocity vector of the particle and ##\mathbf B## the magnetic field vector.
At least the math for effects of magnetic fields is fairly straightforward :). And the reasons/explanations for the "perpendicular to velocity" part also has quantum underpinnings, right?

Also how do i know what is affected by magnetic fields? Magnetic fields still only affect things on the basis of them having a positive or negative charge, right? They just affect them in a different way because the physics of particles being in motion change the mechanics? And permanent magnets are tied into, and affected by those same principles?
Then there must be some similarities on the quantum level between magnetic fields generated by motion of a charge and stationary magnetic fields of permanent magnets?

Quote by Jano L. 					 				 				Yes, it depends on the frame of reference. So does the magnetic and electric field.  If you had two charges moving along with the same velocities, from your point of view, they would be surrounded by magnetic fields, but from their point of view, there is just electrostatic field and no magnetic field.
So then does that mean the outcome of the observation is relativistic too? From their frame of reference would they only be affected by electrostatic fields, whereas from my frame of reference i would see it unfold as though they had been under the influence of a magnetic field?

Electric and magnetic field are just two parts of description of interaction between bodies. "How much" of the interaction is described by electric force and how much by magnetic force depends on the frame of reference.
So unless I'm mistaken, it's the same set of rules (in the sense that it's a matter of attractive and repulsive forces), but the mechanics and manifestations of particles when in motion unfold differently from when at rest? And the explanations for why are mostly Q.E.D based?

Quote by jtbell 					 				 				[I took too long to write this, and Jano slipped in before me.]    Yes indeed! And so is the distinction between electric and magnetic fields.   Consider two stationary charges, one above the other from your point of view as you stand in front of them, and separated by some distance. Each charge produces (only) an electric field, which exerts an electric force on the other charge. If the charges are free to move, they move towards or away from each other depending on whether they are "like" or "unlike" charges.  Now imagine running past the two charges. From your new point of view, the charges are both in motion. In addition to the electric fields and forces, each charge now produces a magnetic field which exerts a magnetic force on the other charge.  Clearly the net effect of the electric and magnetic forces in the second case must be the "same" as the effect of the electric forces in the first case, in terms of the motion of the charges, after taking into account the the difference in your own motion. After all, the charges don't "know" whether you're standing still or running.   We say nowadays that electric and magnetic fields and forces are merely different aspects of a single unified electromagnetic field and electromagnetic force. If we know the electric and magnetic fields in one reference frame (e.g. the one you use when you're standing still), and the relative velocity of another reference frame (e.g. the one you use when you're running), we ought to be able to calculate the fields in the second frame. That is, we ought to be able to transform the fields from one frame to the other.  The question of how to do this in a way that is consistent with how the laws of mechanics transform between reference frames, was a major theoretical puzzle in the late 1800s, which led ultimately to Einstein's Special Theory of Relativity.
I had no idea that electromagnetics had so many relativistic components! So, correct me if i'm wrong, but let's say you're running towards the charges and observing an electric field:

There is one true underlying reality in regards to their actual state. To arrive at that state, various observers at various speeds will view differently rendered versions of the same event, witnessing varying proportions of electric and magnetic fields in use (depending on their speeds?), which all reconcile the event with it's true mathematical reality, where the specific nature of the "reconciliation" is based on their frame of reference?

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Quote by mpatryluk 					 				 				There is one true underlying reality in regards to their actual state.
No. There is no "true underlying reality". That's precisely what this effect demonstrates. According to ANY observer, moving in ANY way, the particles will behave exactly the same and will either move apart if they are like charges or towards each other if they are opposite charges.

Quote by Drakkith 					 				 				No. There is no "true underlying reality". That's precisely what this effect demonstrates. According to ANY observer, moving in ANY way, the particles will behave exactly the same and will either move apart if they are like charges or towards each other if they are opposite charges.
Ok, but if they were moving relative to me, i would observe a magnetic field. Yet relative to each other, they would be stationary and observing an electrostatic field. So no matter what vector of movement i was on, i would view them do the same thing? So i would perceive it as a magnetic field but the interactions i observed between the two would be that of a static field?

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