### Question

How are all magnetic fields produced? Where are the moving charges in the iron atoms of a magnet?

Asked by: Robert Reeves

### Answer

All magnetic fields result, in one way or another, from **moving charges**. Although allowed by Maxwell's equations, which mathematically relate electric and magnetic fields via the source charges and currents (moving electric charges), the '**magnetic monopole**' has **never been observed**. If it existed, it would be a particle responsible for the creation of a magnetic field absent an electric current.

To the specific question of where are the moving charges in the iron atoms of a magnet, there are two sources. The first is in the **orbital motion** of the electrically charged electrons around the nucleus. The second is, speaking classically, due to the charge distribution on the electron and the fact that the electron has '**spin**.' That is, you can think of the electron as a ball with charge distributed over its surface. When the ball spins, that charge is set in motion around the electron's spin axis, resulting in a magnetic field specific to the electron, independent of its orbital motion. The latter is referred to as the spin magnetic moment of the electron.

The orbital and spin components of the magnetic field combine in what is called the spin-orbit interaction to produce the overall magnetic field of the iron atom.

In fact, the above 'classical' explanation of the magnetic moment of the electron **is inaccurate** and is only **suggestive**. Very serious problems arise if the charged rotating ball model of the electron is taken too literally, not the least of which is due to the fact that the electron has no known radius. That is, as far as has ever been observed experimentally, the electron behaves as a true mathematical point, or singularity, without a measurable radius. The magnetic moment, or field, of the electron arises for more subtle reasons based in **quantum mechanics** and the **quantum theory of fields**.

Answered by: Warren Davis, Ph.D., President, Davis Associates, Inc., Newton, MA USA