Electron Magnetic Moment

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Question:

As I understand it magnetic fields arise from moving charges. This I understand and even know how to calculate using laws like Biot-Savart. My question doesn't concern that though. I've heard that electrons have magnetic fields while at rest. What I'm having a problem with is calculating that. If an electron is at rest then putting something like "qv" into the Biot-Savart law will lead to a zero field because "qv" is equal to zero. Is there an equation that would allow me to calculate the force between two electrons at rest from their inherent magnetic fields? And if so can you describe the terms and units to be used in the equation?


Answer:

The magnetic field of an unmoving electron is due to its intrinsic magnetic dipole moment. In quantum mechanics, this dipole moment is related to the spin of the electron. Note, however, that the electron is not spinning per se. These is a quantum mechanical effect with no classical analogy.

The magnetic dipole moment of an electron is −9284.764 × 10^{-27} J/T. You can find this value and others here.


The magnetic force between two stationary electrons is due to the force between to magnetic dipoles. You can find a description of magnetic dipoles and the forces between them here.

-Michael Shay