# What is the magnetic moment, and what does it have to do with the spin of the electron? [closed]

So when an object spins (like the electron), it is said to have a magnetic moment. Now, I do not understand what they mean when they say that it has a magnetic moment.

When I did research, I saw this picture from which I assumed that the magnetic moment is nothing but the magnetic field of the electron. Is my this hypothesis wrong?

I also read that spin up and spin down refer to positive and negative magnetic moments. If this is the case, then clearly a magnetic moment is not a magnetic field.

So I am getting very confused as to what a magnetic moment for an electron means.

## closed as unclear what you're asking by ACuriousMind♦, Jon Custer, user36790, Sebastian Riese, GertOct 10 '16 at 2:45

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• What about e.g. the Wikipedia article about magnetic moments is unclear to you? Can you be more specific about what you do not understand? – ACuriousMind Oct 8 '16 at 21:47
• Having an electron and a positron (the anti-particle of the electron) with same alignment of their magnetic fields there spin will be in opposite directions. Additional keep in mind that due to the Einstein-de Haas-experiment the spin has really to do with a angular momentum. – HolgerFiedler Oct 8 '16 at 21:53
• @ACuriousMind I am confused as to wether magnetic moment is just another word for magnetic field of an electron or if it means something else (like the direction of the magnetic field) – user510 Oct 8 '16 at 22:20

It's that the electron has a magnetic dipole moment. It's akin to an electric dipole moment inasmuch as it generates a magnetic field that behaves similarly to an electric dipole field (falls off like $1/r^3$). Unlike electricity, which has net electric charge as a monopole moment, the lowest order moment possible in magnetism that obeys Maxwell's equations is the dipole moment. For more details about the magnetic multipole expansion go here. Note that the idea is that a multipole moment generates a multipole field of the matching sort, and any generic field can be approximated by a sum of multipole fields, in the appropriate region (e.g. outside of all of the charges/currents generating the field).
The physics 102 formula for calculating the dipole moment of a flat current carrying loop of wire is:$$\mathbf{\mu} = I A \mathbf{n},$$ where $I$ is the current, $A$ is the area of the loop, and the direction of the unit vector, $\mathbf{n}$, is fixed by a right hand rule. More generally, it is possible to show that the magnetic dipole moment is proportional to a charge carrier's angular momentum, and hence the connection to spin.