Electrical Current Repelling Magnets Due to Relativity

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I recently watched this Varitasium video where he explains the magnetic field due to a current carrying wire.

In the video he explains how what we see and describe as the magnetic field produced by a current carrying wire is actually just a electric force caused by the an imbalance of charges which caused by contraction due to relativistic speeds of moving charges. The example he gives repels an ion, which made sense to me, but why would that electric force repel a magnet? Also, it does't explain the direction of the magnetic force produced by a current carrying wire.

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Electric and magnetic fields turn out to be components of the electromagnetic field. Different frames of reference break the electromagnetic field down into electric and magnetic fields in different ways. So you are wrong to say that the magnetic field is "actually" an electric field. They are just two different descriptions of the same thing.

I'm not quite sure what you think this doesn't explain. I suspect the direction you are missing comes from the velocity of the ion in the electron rest frame. But I'm not sure if that is you are worrying about.

Mentor
but why would that electric force repel a magnet?
The electric force would not repel a magnet. In that frame there is still a current, and that current still produces a magnetic field. That magnetic field is simply ignored for the stationary charge since it produces no force on it, but it is there and you cannot ignore it for the magnet.

I'm not quite sure what you think this doesn't explain. I suspect the direction you are missing comes from the velocity of the ion in the electron rest frame. But I'm not sure if that is you are worrying about.

In the video the cat is accelerated down by a current running to the right, but a magnetic force due to the current would have accelerated the cat into the paper. That's what I don't understand.

Mentor
In the video the cat is accelerated down by a current running to the right, but a magnetic force due to the current would have accelerated the cat into the paper. That's what I don't understand.
The direction in the video is correct. In the rest frame of the wire there is a magnetic field normal to the paper and the cat’s velocity is horizontal. The magnetic force is perpendicular to both, so that is vertical.

Cardinalmont
The direction in the video is correct. In the rest frame of the wire there is a magnetic field normal to the paper and the cat’s velocity is horizontal. The magnetic force is perpendicular to both, so that is vertical.

Thank you! This makes great sense to me! There is last unclarity that still remains to me. The phenomena is described when the cat(ion) is moving at the same velocity as the current. In the cat's perspective the protons are moving and are therefor contracted caused this repulsive force, but why doesn't the opposite happen when the cat is still? Why don't the moving electrons in the current contract and attract the cat?

Mentor
why doesn't the opposite happen when the cat is still? Why don't the moving electrons in the current contract and attract the cat?
It certainly could be arranged that way. The result of what you describe would be that the wire would be negatively charged in the lab frame. The experimenter could accomplish this by putting a strong negative voltage on both ends of the wire.

For simplicity the video just covers the case where the wire is neutral in the lab frame so the charge density is zero in the lab frame.

Cardinalmont
jartsa
It certainly could be arranged that way. The result of what you describe would be that the wire would be negatively charged in the lab frame. The experimenter could accomplish this by putting a strong negative voltage on both ends of the wire.

For simplicity the video just covers the case where the wire is neutral in the lab frame so the charge density is zero in the lab frame.

I came up with this question. Obviously I think I know the answer. But what do you guys say?

Electrons inside a negatively charged rod start to move - test charge next to the rod does not react. (Battery terminals were connected to rod ends)

A negatively charged rod start to move - test charge next to the rod does react. (Rod was kicked gently pushed, no deformation of rod occurred)

How do we explain the difference?

Let's say that amperage is the same in both cases.

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Cardinalmont
jartsa
Electrons inside a negatively charged rod start to move - test charge next to the rod does not react. (Battery terminals were connected to rod ends)

A negatively charged rod start to move - test charge next to the rod does react. (Rod was kicked gently pushed, no deformation of rod occurred)

How do we explain the difference?

We know from the Veritasium video, and from other sources, that a test charge reacts to length contraction of nearby charge formations.

We know from experiments that a still standing test charge does not react to changes of amperage caused by free electrons flowing inside a conductor. From that we conclude that there is no length contraction of that formation of particles.

We know from experiments that a moving test charge does react to changes of amperage caused by free electrons flowing inside a conductor. So we conclude that there is length contraction of that formation of particles in the rest frame of the test charge.

So there is one frame where the formation of the free electron does not have any density change associated with a velocity change. Let us ponder that special frame.

I think it is the frame where the plus terminal of the battery starts to absorb electrons at the same time as the minus terminal starts to emit electrons. That is the rest frame of the battery. Usually the rest frame of the battery is also the rest frame of the wire connected to the battery. It must be the battery that defines the one special frame, because a wire with an electric current in it does not have a well defined rest frame.

(I though that this would be much more simple)

Cardinalmont