# Does a stationary electron have a magnetic field?

1. Jun 8, 2013

### falcon32

At first glance, it seems that, no, a stationary electron would not have a magnetic field associated with it, since we know that fields arise because of moving charges.

However, if I understand the current description of the electron, it has an inherent quantum property called spin. This is nothing like what we normally think of, as in the spinning of a classical sphere around an axis of rotation (since then the electron would need to be spinning with an angular velocity far greater than the speed of light, which is impossible), but nevertheless, can give rise to a magnetic moment.
(http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html)

But aren't magnetic moments associated with respective magnetic fields via the Biot-Savart Law? For example, we see that earth has both a magnetic moment, and a related field; in fact everywhere we see magnetic fields, and we can find out their related magnetic moments.
(http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/biosav.html)

So does an electron have an associated magnetic field because of its inherent quantum property of spin?
And if it does not, then why does it display this deviation from what seems to be a dual relationship seen throughout nature?

Thanks for helping me figure this out.

(note: this is an unanswered question from one of my previous threads)

2. Jun 8, 2013

### The_Duck

A magnetic moment that doesn't produce a magnetic field is a contradiction in terms. A stationary electron does have a magnetic moment, which produces a dipole magnetic field around the electron. The magnetic moment is aligned with the electron's spin, and the two are related. I think that in general any charged particle with nonzero spin will have a magnetic moment aligned with its spin.

A spinning classical charged sphere of finite radius also has a dipole moment aligned with its spin and will generate a magnetic field. If you try to model the electron as a classical sphere like this, however, you will predict the wrong value for the gyromagnetic ratio.

Last edited: Jun 8, 2013
3. Jun 8, 2013

### falcon32

Ok awesome, thanks for clarifying that...I had suspected as much, but was worried that if I out and said it, someone would bite my head off for being wrong, so I phrased it as a question. My head takes time to regrow :)