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I am trying to understand the concept of a particle's magnetic moment being 'positive' or 'negative'...

From what I understand, a negative magnetic moment means the particle's inherent 'spin' is pointing in the opposite direction of its magnetic moment... But what does that mean in terms of 'observable' properties?

Quantum 'spin' was discovered by Stern and Gerlach when they discovered that particles have an inherent magnetic moment, so... A particle's spin IS, first and foremost, it's magnetic moment...

Edit: P.S: How does this apply to neutrons, which are chargeless, yet have a 'negative' magnetic moment? How can it be 'antiparallel', as compared to the proton?

So, how can a particle have a 'direction' to its magnetic moment in the first place, and how can it be opposite to its inherent angular momentum (spin)?

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Suppose your "particle" is actually a positively-charged sphere. Spin the sphere about some axis and the moving charges generate a magnetic field. You can use the Biot-Savart law to figure out that the direction of the magnetic field along the rotation axis will be parallel to the angular momentum.

Switch to a negatively-charged sphere, and you reverse the relationship between the direction of rotation and the direction of the current. For a negatively-charged rotating sphere, the magnetic field along the axis of rotation is antiparallel to the angular momentum vector. That's what we mean when we say that a particle has a negative magnetic moment.

(A "rotating charged sphere" is not a very good model for a quantum-mechanical spinor, but it works in this case.)

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  • $\begingroup$ How does this apply to neutrons, which are chargeless, yet have a 'negative' magnetic moment? How can it be 'antiparallel', as compared to the proton? $\endgroup$
    – Kurt Hikes
    Jul 2, 2021 at 23:22
  • $\begingroup$ The Earth is electrically neutral and has negative magnetic moment. Earth's angular momentum vector is parallel to its axis of rotation and points north; Earth's magnetic field exits the planet in Antarctica and re-enters near the Arctic. (At midlatitudes the dipole return field points to the north, which is why compasses work the way they do.) The sign of the magnetic moment relates field direction and spin direction. A net electric charge is just one of several ways for a spinning object to generate a magnetic field; it is a right-hand-rule convenience that the signs work out the right way. $\endgroup$
    – rob
    Jul 3, 2021 at 0:13
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If a spinning body has an equal amount of positive and negative charge --- so that total charge zero --- and the negative charge is further from the rotation axis than the positive charge, then the resulting magentic moment points in the opposite direction to the spin.

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