# Force From Spin Magnetism

*Most recent answer: 07/17/2015*

- John (age 44)

Phenix City, AL U.S.

Sure. The force depends on how the intrinsic magnetic dipole moments of the spins are oriented with respect to each other and to the direction between them. For a given set of directions, the force falls off as the inverse of the fourth power of the distance.

The magnetic dipole-dipole interaction is described in detail here: https://en.wikipedia.org/wiki/Magnetic_dipole%E2%80%93dipole_interaction in conventional but irritating Standard International units. Here's a link that gives the interaction energy in nicer CGS units: http://http://userpage.chemie.fu-berlin.de/~tolstoy/chapter3.pdf. To get the force you just take minus the derivative with respect to the distance between them. In CGS units, the magnetic moment of an electron spin is about 10^{-20} erg/Gauss (https://en.wikipedia.org/wiki/Bohr_magneton). So, depending on the orientations, the magnitude of the force between two such spins at distance r is around 10^{-40}/(r/cm)^{4} dynes. (The notation means to give r in cm.)

The electrical force is around 25*10^{-20}/(r/cm)^{2 }dynes. So even on atomic-scale distances (10^{-8} cm) the electrical force is much bigger. The reason you can sometimes notice magnetism is that materials are usually about electrically neutral, but in some materials the electron spins tend to line up so that their fields add up.

Mike W.

*(published on 07/17/2015)*