# Spin and magnetic field

• Gavroy
In summary, the conversation discusses the concept of spin, particularly in relation to its direction and its effect on a magnetic field. It is mentioned that an electron's spin has two possible values for the z-direction, but its direction in space is arbitrary. There is a question about the existence of an equation that gives the magnetic field in terms of an electron's spin, but it is noted that this may be challenging to apply due to the boundary between classical and quantum mechanics. The conversation also touches on the idea that the direction of an electron's magnetic moment can only be determined once an axis is chosen, and that in quantum mechanics, only one value can be measured at a time.

#### Gavroy

hi

unfortunately, i have still some troubles to understand the concept of spin and wanted to get things right now, so maybe someone of you could help me:

let me start with an electron, which is a spin 1/2 particle and has therefore two possible values for the z-direction of the spin: -h/(4π) and +h/(4π)

does this mean, that the direction in space of the spin is completely arbitrary and only the absolute value of the spin is determined?

i heard that a spin causes a magnetic field. is there anywhere an equation that gives me the magnetic field in terms of a free electron with arbitrary spin?(just for curiousity)

am i correct by saying that only based on the fact that there are two possibles for the z direction, this does not mean, that if you have two electrons with the same spin, that they cause the same magnetic field, as it is impossible to determine the x and y direction of the spin and therefore the contribution of these two directions to the magnetic field? (i guess this would also mean that the answer to my question, if there is a general equation that gives me the magnetic field in terms of the spin, would be that this is not so)

is there are reason that you have an energy yield, when you have positive spin quantum number in z-direction and a homogenous magnetic field in this direction or does this have anything to do with attrative forces between the magnetic field caused by the spin and the magnetic field of the field?

and again i am sorry about my english, i am still practising.

believe it or not, i read both of them...and i still do not know the answer to my questions. but thanks anyhow

you can lead a horse to water but you can't make him drink.

i am glad that it is at least a horse and not a donkey in your metaphor

by the way, i do not see anywhere on these pages only one sentence, that tells me somethng about whether there is an equation that gives me the magnetic field in terms of the particle's spin.

Gavroy said:
i heard that a spin causes a magnetic field. is there anywhere an equation that gives me the magnetic field in terms of a free electron with arbitrary spin?(just for curiousity)

An electron's spin is associated with a magnetic dipole moment:

http://en.wikipedia.org/wiki/Electron_magnetic_dipole_moment#Spin_magnetic_dipole_moment

In classical electromagnetism, a magnetic dipole moment produces a magnetic field as follows:

http://en.wikipedia.org/wiki/Dipole#Field_of_a_static_magnetic_dipole

However, I would be cautious about applying this to a single electron which is described quantum-mechanically. The boundary between classical electrodynamics and quantum electrodynamics is tricky to navigate. :uhh:

okay, but is it still right, that you cannot say something about the direction of the magnetic moment?-and only about its absolute value?

Gavroy said:
okay, but is it still right, that you cannot say something about the direction of the magnetic moment?-and only about its absolute value?

You can tell the direction of the magnetic field as soon as you choose an axis and measure it's value relative to that axis. That's not even different from spin in classical mechanics (=angular momentum of an object in its rest frame) only that in qm you will only measure one of two possible values while in classical mechanics you will find one value out of a continuum of possible values. However as long as you don't have measured spin, it's value will also be undetermined in classical mechanics.
In QM you can also only measure the value of spin along one axis without destroying the information from previous measurements along other axes (that's strictly true only for spin 1/2, for higher spins, the behaviour becomes more and more classical).