Magnetic Moment of an Electron

[Antuanne]

I am sort of new to physics and have an interest in particle physics. I was trying to figure out what "magnetic moment" of an electron is and I saw this picture and I am wondering if I am correct about something.
In the diagram I have supplied, does the arrow μ or the circle represent the magnetic moment of a particle? Trying to figure this out. And could this diagram apply to an electron? If not, what's the difference between and electron's and this?

 

[Simon Bridge]

In the diagram I have supplied, does the arrow μ or the circle represent the magnetic moment of a particle?

The arrow.

could this diagram apply to an electron?

Sort of - though electrons do not have an asymmetric charge distribution to give you the circle part.

 

[Antuanne]

How is the magnetic moment of something measured? Is it θ measured or the are of the circle or what?

 

[Vanadium 50]

How is the magnetic moment of something measured?

See: http://en.wikipedia.org/wiki/Magnetic_moment

 

[Simon Bridge]

How is the magnetic moment of something measured? Is it θ measured or the are of the circle or what?

... you measure the magnetic moment of something by looking at it's response to an applied magnetic field.

 

[AJ Bentley]

Magnetic moment is an idea derived from ordinary magnets.
A magnet has two poles separated by a distance. The magnetic moment is simply the strength of the poles multiplied by the distance between them.

It comes from the fact that compass magnets will turn north/south in a field and the magnetic moment gives a measure of the turning force.
It gets it's name from the ordinary 'moment of a force' about a fulcrum.

Electrons and some other fundamental particles also have a magnetic field that comes from the fact that they are spinning. That's why we sometimes draw a circle, sometimes an arrow to represent the axis of spin.

 

[Simon Bridge]

Electrons and some other fundamental particles also have a magnetic field that comes from the fact that they are spinning. That's why we sometimes draw a circle, sometimes an arrow to represent the axis of spin.

That is a common mistake - electrons do not literally "spin", that is just another bit of jargon to say it has a magnetic moment. The spin of a fundamental particle is a QM property.
Also see: http://scienceblogs.com/principles/2010/07/26/electron-spin-for-toddlers/

 

[AJ Bentley]

That is a common mistake - electrons do not literally "spin", that is just another bit of jargon to say it has a magnetic moment. The spin of a fundamental particle is a QM property.
Also see: http://scienceblogs.com/principles/2010/07/26/electron-spin-for-toddlers/

This is a simple question, asked at a high-school level. Dragging in the subtleties of QM is unnecessary and damaging.

For all intents and purposes, it's spin. It's certainly not a 'mistake' to say so, any more than it's a mistake to say 'a particle at x moving with velocity v' at the same level.

 

[andrien]

But electron is a point particle.How can it spin.

 

[AJ Bentley]

But electron is a point particle.How can it spin.

rofl! The logic is undeniable!

 

[Simon Bridge]

This is a simple question, asked at a high-school level.

It is unlikely being asked at HS level since this topic is seldom covered at HS level. It is reasonable to consider that OP is reading ahead of his level and is trying to make links with his prior learning.

Dragging in the subtleties of QM is unnecessary and damaging.

All teaching is potentially damaging - in this case, there is more damage in leaving them out. The "subtleties" involved are not, in practise, a problem for HS students capable of asking the question. It is not a problem for HS students to realize that the electron "spin" is not a literal spinning like a top. Did you have a look at the link I supplied? It should bridge the concepts in a way accessible to HS students.

For all intents and purposes, it's spin. It's certainly not a 'mistake' to say so, any more than it's a mistake to say 'a particle at x moving with velocity v' at the same level.

But you did more than that - you modeled the electron spin as that of a macroscopic object with an uneven distribution of charge without any cautionary note about the misunderstandings that are commonly found on PF that result from this image.

I cover QM issues, briefly, in my HS class when they come up. I make a distinction between classical and "modern" physics and try not to mix them up. This, particular, mixup results in a lot of questions on PF and elsewhere involving misunderstandings of spin.

Anyway HS students are capable of questions like:

But electron is a point particle. How can it spin?

One of the complexities in modern teaching (what with the internet, science TV, and all) is that the teacher can no longer rely on the separation of different levels of explanation. It is more important than ever to try to anticipate future problems... especially considering how pseudoscience scams like to exploit them.

There is, naturally, a balance to be struck with the students level of understanding when answering these things - when I feel that a classical model is more appropriate I will preface the model with a note that it is a classical one and that there are others. That usually helps avoid some confusion later and the student has the option to ask for a more advanced model if they feel up to it.

But there is no need to squabble over pedagogy - in an open forum it is certain that several approaches will be attempted. There is no "one true path" to learning or teaching. Here, two approaches have been presented and discussed, thus any perceived or anticipated harm should be mitigated. To recap:

Classically: the electron acts, to HS level, as though it is a spinning object.
For the future: the student is cautioned against thinking of this as a literal spin.
No problem.

 

[AJ Bentley]

Teaching has changed since my day - I haven't taken a class since the 70's. but I still think a chronological explanation helps with such questions as :-
'Why do we call it spin if it isn't spin?'

Anyway, I'm not sure that you can say it isn't literal spin.

Certainly in the case of a photon, the spin is quite literal, being the helical rotation of the E and B vectors. I haven't yet studied string theory in any detail but I fully expect to find that electron spin can be 'explained' similarly.

 

[Simon Bridge]

Anyway, I'm not sure that you can say it isn't literal spin.

In the sense that it is not a classical "spin" yes. It shares characteristics, hence the name. It is seldom helpful to imagine photons as being like little tops even if you can make something turn by hitting it with them.

Teaching has definitely changed - so has learning - I blame the internet.
I trained in the good old days when it made sense to ban calculators from exams and students couldn't just google their homework. OTOH: I think it's great - students can follow their noses a lot more. There is an increased emphasis on critical inquiry and investigation skills. The teachers job becomes one of equipment and navigation.

I think we need to hear from OP :)
@Antuanne: still confused?