Electron Spin and current-induced magnetic fields

[atommo]

Hi,

I'm currently investigating magnetic fields/their cause. This has inevitably led me to learn all about electrons. Here I want to post my understanding on electron 'spin' so people can correct me if I'm wrong/help others get a better understanding.

So I watched this YouTube video for research:


From what I understand, 'electron spin' is not an actual spin, but which way an electron attracts/repels. Since electrons exist as quantum particle clouds (and in the video it describes electrons as infinitely small points at ~7:20) 'spin' isn't really a thing they do.

Essentially half electrons attract one way and half attract the other. It doesn't matter which orientation they are being tested in: it will always be roughly 50/50.

This leads onto a big question: in a wire where electrons travel, why does the magnetic field induced always go anticlockwise if the electron current is flowing towards you? Surely if quantum mechanics dictates a 50/50 on electron spin, wouldn't it be a 50/50 chance the magnetic field would spin the other way?

Maybe there's an answer to this or maybe this is one of science's yet-to-be-answered questions. It would be useful to know why if possible though.

 

[Orodruin]

which way an electron attracts/repels

This is not a very accurate description. The spin is the electron angular momentum. The electron's magnetic dipole moment is proportional to its spin.

This leads onto a big question: in a wire where electrons travel, why does the magnetic field induced always go anticlockwise if the electron current is flowing towards you? Surely if quantum mechanics dictates a 50/50 on electron spin, wouldn't it be a 50/50 chance the magnetic field would spin the other way?

The magnetic field of a wire that carries a current is not due to the spin of the electrons, it is due to their motion.

 

[Drakkith]

This leads onto a big question: in a wire where electrons travel, why does the magnetic field induced always go anticlockwise if the electron current is flowing towards you? Surely if quantum mechanics dictates a 50/50 on electron spin, wouldn't it be a 50/50 chance the magnetic field would spin the other way?

The magnetic field in a current-carrying wire is caused by the motion of the charges, not their spin. The full explanation delves into special relativity and gets very counter-intuitive though, so don't expect an easy answer if you're trying to find the fundamental reason that a magnetic field is created.

 

[atommo]

The magnetic field in a current-carrying wire is caused by the motion of the charges, not their spin. The full explanation delves into special relativity and gets very counter-intuitive though, so don't expect an easy answer if you're trying to find the fundamental reason that a magnetic field is created.

Thanks for clearing that up for me- are there any good links for reading into this?

 

[Drakkith]

Thanks for clearing that up for me- are there any good links for reading into this?

Here's a couple that turned up on Google that I thought were okay:

http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html
http://www.chip-architect.com/physics/Magnetism_from_ElectroStatics_and_SR.pdf
http://physics.weber.edu/schroeder/mrr/mrrtalk.html

If you can't do the math, just try to focus on their results.

 

[teragreg]

Hi! Did you ever get your answer? I’m trying to understand why it’s always clockwise relative to the direction of current.

 

[Dale]

Hi! Did you ever get your answer? I’m trying to understand why it’s always clockwise relative to the direction of current.

It is clockwise because most people are right handed so clockwise follows a right hand rule. If most people were left handed we could have used a left handed rule and the physics would be fine. A left hand rule would make it counter clockwise

 

[teragreg]

Thanks so much for the speedy reply!

What I meant was why is the field itself clockwise around a current carrying wire? We can experimentally verify this by a compass, which at idle points to earth’s north, then a current above runs and the compass will always snap into a position where north points clockwise around the current.

I understand why we use the hand we do, but why does the universe work this way?

 

[Sagittarius A-Star]

I understand why we use the hand we do, but why does the universe work this way?

The sign of the electron-charge and the current-direction/sign are a matter of convention. This doesn't change physics.

The (frame-dependent) magnetic components of the electromagnetic field-tensor are a relativistic effect.

Lorentz-force:

• The 4-force on a charge is this charge divided by $c$, multiplied with the electromagnetic field-tensor and the 4-velocity of the charge.$$F_\mu = {q \over c}E_{\mu\nu} U^\nu$$

Maxwell's inhomogeneous equation(s):

• The "4-dimensional divergence" of the EM-field-tensor is a constant, multiplied with the 4-current.$$\partial_\mu E^{\mu\nu}={4\pi \over c}J^\nu$$

Source, see equations (38) and (47): http://www.scholarpedia.org/article...etism#Maxwell.E2.80.99s_Theory_in_Tensor_Form

 

[teragreg]

Hi there. I don’t mean to belabour the point, but I’m really not talking about the convention. Pick a convention, any convention, the magnetic field will always be in this direction given the same direction of current. Again, not speaking about convention. Use the earth’s field as a reference for example. The question is why this way, and not the other?

 

[Sagittarius A-Star]

Hi there. I don’t mean to belabour the point, but I’m really not talking about the convention. Pick a convention, any convention, the magnetic field will always be in this direction given the same direction of current. Again, not speaking about convention. Use the earth’s field as a reference for example. The question is why this way, and not the other?

Maybe the following video makes it clear.

In the wire's restframe, the cat must be repelled from the wire by it's magnetic field, because:

• In the cat's restframe, the cat is repelled by the wire's electric charge.

 

[teragreg]

That’s great and explains why a field is generated. Fantastic.

Perhaps we’re miscommunicatinf through text, but I’m talking about the direction of the field generated - this is a very real direction.

If this following point get across, we will not be able to proceed in our discussion:

Get a car battery and hook up a wire and get ready to pass a current though it. Ensure you know which way the current is actually flowing. Don’t worry about convention yet. Now get a magnetic needle on a swivel and let it adjust to earth’s field. Mark one side north, this is now your “convention.” Not pass a current through the wire. Whatever side you marked as north will now snap into position around the current showing that the magnetic field around current itself Is pointing north as clockwise.

The question is why does the actual universe itself, not the human convention, point clockwise around a current? Again. You can use whatever convention you want as long as it’s consistent. What makes it this way, and only this way, every single time?

 

[Orodruin]

but I’m talking about the direction of the field generated - this is a very real direction.

It is not. As has been hinted to, this is a matter of how you define the field direction. You could just as well have gone with painting the other end of the compass red. A sign might change here and there, but the physics will be the same in the end.

 

[teragreg]

Thank you for your time!

 

[Ibix]

The question is why does the actual universe itself, not the human convention, point clockwise around a current?

You can ask why the compass points in the direction it does rather than the opposite, but this isn't the same as asking why it points clockwise. The former is because the fields align; the latter involves defining a convention for which way a magnet is pointing.

 

[teragreg]

You can ask why the compass points in the direction it does rather than the opposite, but this isn't the same as asking why it points clockwise. The former is because the fields align; the latter involves defining a convention for which way a magnet is pointing

Thanks for the correction. I believe you understand the question I’m asking! Do we know why it points this way and not the other?

 

[Ibix]

Thanks for the correction. I believe you understand the question I’m asking! Do we know why it points this way and not the other?

Because that way the fields align and the total energy is at a minimum.

 

[Sagittarius A-Star]

That’s great and explains why a field is generated. Fantastic.

Perhaps we’re miscommunicatinf through text, but I’m talking about the direction of the field generated - this is a very real direction.

Not really. The video "explains" the direction, into which the charged cat, moving with respect to the wire rest frame, is accelerated by the field.

This "explanation" refers to the physical effect, that in electrostatics charges with same sign repel each other (and do not attract each other).

 

[Dale]

the direction of the field generated - this is a very real direction

The direction of the field is not a real direction. The direction of the magnetic field is a convention, specifically the right hand rule.

Ensure you know which way the current is actually flowing. Don’t worry about convention yet.

There is already a convention in the direction the current flows. This is a different convention, specifically the convention that the proton is positively charged.

What is not a convention is that two wires with parallel currents experience an attractive force. Regardless of which convention you pick for the sign of the charges and regardless of which direction you choose for the magnetic field, this fact holds.

As @Ibix said, this happens because with parallel currents the total energy stored in the magnetic field decreases as the wires get closer.

All other questions that are actually independent of the conventions can be traced to this fact. For example, the alignment of the compass needle that points roughly in the direction of Polaris can be used to infer the presence of a bound current on the needle. This bound current produces attractive or repulsive forces when placed near current carrying wires as above.