Do electrons produce a constant magnetic field?

[Astronaut]

I read somewhere that electrons produce constant magnetic field when moving with constant velocity. But I think it is not true.I thought a reason for it

Imagine that an electron is stationary and I am moving with a constant velocity.
In my respect electron is moving, so, it should produce magnetic field. But in ground frame electron should not.
This is a contradiction as both frames of references are inertial.

Hence electron should not produce magnetic field.Am I wrong or electron actually doesn't produce constant magnetic field?

 

[nitsuj]

I saw somewhere that a moving (or was it accelerating?) electron emits light!

 

[Dale]

In my respect electron is moving, so, it should produce magnetic field. But in ground frame electron should not.
This is a contradiction as both frames of references are inertial.

You are half right. The electron does indeed produce a magnetic field in your frame and does not produce a magnetic field in the ground frame. However, it is not a contradiction but simply a proof that the magnetic field is frame variant. No observed results will actually be contradictory.

 

[Astronaut]

You are half right. The electron does indeed produce a magnetic field in your frame and does not produce a magnetic field in the ground frame. However, it is not a contradiction but simply a proof that the magnetic field is frame variant. No observed results will actually be contradictory.

This seems very odd to me .
This happens only with magnetic field?

 

[Drakkith]

This seems very odd to me .
This happens only with magnetic field?

No, as velocity increases, the electric field is seen more and more as a magnetic field. At very high velocities nearly all of the interaction between the moving particle and an observer will be seen as a magnetic field, with little contribution from the electric field.

 

[Dale]

This seems very odd to me .
This happens only with magnetic field?

It is very odd, but it is the way the universe works. This is due to Relativity. And no, it is not only with the magnetic field. Time and space are relative. Energy and momentum are relative. Electric and magnetic fields are relative. Charge density and current density are relative. Frequency and wavenumbers are relative. And so forth.

 

[PeroK]

I read somewhere that electrons produce constant magnetic field when moving with constant velocity. But I think it is not true.I thought a reason for it

Imagine that an electron is stationary and I am moving with a constant velocity.
In my respect electron is moving, so, it should produce magnetic field. But in ground frame electron should not.
This is a contradiction as both frames of references are inertial.

Hence electron should not produce magnetic field.Am I wrong or electron actually doesn't produce constant magnetic field?

Isn't this the very question that led Einstein to the Special Theory of Relativity? And the question that the opening paragraph of the 1905 paper addresses?

 

[Astronaut]

It is very odd, but it is the way the universe works. This is due to Relativity. And no, it is not only with the magnetic field. Time and space are relative. Energy and momentum are relative. Electric and magnetic fields are relative. Charge density and current density are relative. Frequency and wavenumbers are relative. And so forth.

but i thought that two frames with different velocities are both inertial and are same. Something moving with 0 acceleration and not moving almost have no difference. So i got a little confusion

 

[Dale]

I don't know what you mean by "have a little difference" and "almost have no difference".

 

[Drakkith]

but i thought that two frames with different velocities are both inertial and are same. Something moving with 0 acceleration and not moving almost have no difference. So i got a little confusion

That's the crux of the issue, the very point that we're trying to make. Motion is relative and the field as seen by the electron is purely electric, while the field seen by the observer is part electric and part magnetic because there is relative motion between the observer and the electron. It doesn't make sense because you haven't studied relativity.

 

[tony873004]

A current-carrying wire produces a magnetic field because of the moving electrons. I understand that they do not move very fast (mm or cm/second). If I placed a compass next to a wire in a dc circiut to detect the magnetic field, could I move the compass until it registered no field in order to determine the speed of these electrons? I guess I could try it, but it's easier to ask!

Edit: thinking a little deeper, would I now be registering the field of the moving protons?

 

[Drakkith]

A current-carrying wire produces a magnetic field because of the moving electrons. I understand that they do not move very fast (mm or cm/second). If I placed a compass next to a wire in a dc circiut to detect the magnetic field, could I move the compass until it registered no field in order to determine the speed of these electrons? I guess I could try it, but it's easier to ask!

No, because drift speed isn't a measure of the actual electron speed. Electrons in a conductor normally move around very quickly and in random directions. If you add up the directions and speeds of all of these electrons you find that they average out to a net zero. When a voltage is applied the velocities no longer add up to zero. Instead, you find that there is a net difference between the charges moving in one direction and the opposite. That's the direction of current flow.

Edit: thinking a little deeper, would I now be registering the field of the moving protons?

The protons in a conductor aren't moving. They are locked into the lattice structure of the metal.

 

[tony873004]

I know the protons are stationary with respect to the wire, but relative to an observer on my moving compass, which is moving at drift speed, the average electron speed is now 0 and the protons (in this frame of reference) are moving backwards. Hence, no magnetic field from the electrons, and an equal magnetic field from the protons which are opposite in charge and opposite in velocity (from the moving electrons in the wire's frame of reference) in this frame of reference.

So I'm guessing I can't measure drift speed of a current with a compass.

 

[Drakkith]

Hmm, now you've got me thinking. I'm not sure you would ever register zero magnetic field while current is flowing in a circuit. I just don't know enough to know for sure or explain it.

 

[tony873004]

I don't think I could either. If I moved a compass along a wire that is NOT carrying current, the electrons will produce a magnetic field, and the protons will produce a magnetic field that will cancel it out. For example, the electrons produce a field of +1000 T and the protons -1000 T. Add some current, and the electrons Produce +2000 T and the protons -1000 T for a net of +1000 T. To a stationary observer, this would be electrons +1000, protons 0 = net of +1000. So my original thought experiment was to measure the drift speed with a compass, but now I realize a moving compass won't change anything, regardless of the speed. Too bad! I thought I just came up with a drift speed lab for my high school students.

 

[RacinReaver]

I think this video actually goes into your question halfway decently...

 

[tony873004]

I think this video actually goes into your question halfway decently...

Thanks for the vid. I never knew that.

 

[Dale]

Hmm, now you've got me thinking. I'm not sure you would ever register zero magnetic field while current is flowing in a circuit. I just don't know enough to know for sure or explain it.

Your instinct is correct. B^2-E^2 is an invariant. So, since there is a frame where B is non zero and E is zero this invariant is positive in all frames. The only way for it to be positive is for B to be non zero. So B is non zero in all frames.

 

[FrankJ777]

Interesting video, with nice explanation.
I don't see however how that explains why the magnetic field circulates around the current carrying wire. I thought if you placed a charge particle near a current carrying conductor, the magnetic field would just move it in a circle around the wire at a fixed distance.
The way this video explains the magnet field, it would seem that the magnetic field would point out radially from the wire.

 

[Dale]

You are mixing up the magnetic force and the magnetic field. The two are perpendicular to each other.

 

[FrankJ777]

Yeah, also I was mixing up the force of magnetic and electric fields. I was thinking magnetic fields push charges around like the electric field so that a charge would follow the magnetic field in circles around the conductor. I should have thought about the Lorentz force F = q[E +(v x B)].
Now I can see how the explanation is consistent.
Thanks.

 

[Dale]

No problem, it is an easy mistake to make, and that does make the magnetic field confusing.

 

[FrankJ777]

OK. I have another question referencing the video.
When the charged cat was moving the same speed as the electrons, the protons in the cat's reference frame were moving and the electron were stationary. Due to relativistic effects the "moving" protons contracted and the stationary electrons expanded thereby increasing the positive charge density, and creating a positive electric field, which pushed the charged cat away radially. So why it that when the charged cat is stationary, and there is current of electrons moving relative to the stationary cat, the electron stream does not contract causing the negative charge density to increase and create a negative electric field?
Is it because in current in a wire there is an equal amount of positive charge and negative charge flowing in opposite directions?

 

[Dale]

You have to specify the problem completely in one frame, and then, given that, you apply the rules of relativity to obtain the results in another frame.

So in this case the experimenter sets it up so that in the experimenter's frame the wire is conducting a current and is uncharged. Therefore the fact that the charges are equally spaced in the experimenter's frame is a given. Once you are given that you can use relativity to calculate the situation in another frame, but relativity cannot tell you the first frame.

 

[Drakkith]

So why it that when the charged cat is stationary, and there is current of electrons moving relative to the stationary cat, the electron stream does not contract causing the negative charge density to increase and create a negative electric field?

That is a very good question and probably the hardest to understand about this scenario. I'm going to go outside my comfort zone and attempt to explain this. Hopefully I don't mess it up! (I'm sure someone will slap me if I do ) The following is based off of Bell's Spaceship Paradox:

The key lies in the fact that the electrons are not rigid objects.

Consider a long line of spaceships attached to a frictionless rail that let's them accelerate to any velocity they want. Let's also say that we've placed a light bulb at the starting location of every ship and that there is one ship every 100 meters and that every spaceship is exactly 10 meters long. Now, let's say that each ship accelerates at the same time, at the same rate, until they are all at 0.9c. Crucially, while each spaceship has length contracted to 4.36 meters, the distance between each adjacent ship is still 100 meters! (As long as you measure the distance between each pair of adjacent ships at the same point as you did prior to acceleration.)

Now, let's say that your friend Tom is passing by at 0.9c. What will he see? He will find that each spaceship is 10 meters in length, but the distance between each adjacent ships is now over 229 meters! (The exact reason for this is both conceptually and mathematically complicated and I don't have a chance of explaining it in detail) In addition, he will find that the distance between adjacent light bulbs on the rail is 4.36 meters since he is moving relative to the rail.

Now, let's replace the ships and rail with electrons moving in a copper wire, and replace Tom with a moving positive charge.

From our lab frame, which is at rest relative to our circuit, neither the wire nor the distance between electrons is length contracted. The electrons are like the ships. Even though they are moving and their fields may be length contracted, the distance between them has not changed when viewed from the lab's frame. This is a requirement of our thought experiment since our circuit is not electrically charged. If the electrons were closer together then we would see an electric field and the circuit would indeed be electrically charged.

Now, when we transform our frame of reference to the moving positive charge, we see the wire contract but the distance between electrons increases, meaning that the positive charge density increases and the negative charge density decreases, which add together to push the positive charge away from the wire. From the lab's frame of reference this occurs because of the magnetic field generated by the current, but in the positive charge's frame of reference the wire is now electrically charged.

Also remember that since we have two distinct frames of reference, both viewing two other sets of moving/non-moving objects (negative and positive charges in the wire), it makes this example much more complicated than your basic special relativity problem. I re-wrote this post about 4 times because I myself kept getting it wrong. There are several very confusing concepts here. For one, how can the distance between electrons increase while the wire length contracts? I'm afraid I can't answer that, as it's well outside of my knowledge in this area.

As always, someone please correct me if I'm wrong.

 

[FrankJ777]

Thanks guys.
It's been a while since I've had physics, but I what I think you guys are referring to is "inertial vs non-inertial frames of reference" and "Lorentz transformations"? Do those pretty much cover the concepts you guys are talking about?