The magnetic moment $m$ of a particle is given by $m=kS$, where $k$ is a constant known as the gyromagnetic ratio and $S$ is the particle's spin.
But where does this equation come from? Is it just from experiments?
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$\begingroup$ Did not we once decide to define the ratio as such? $\endgroup$– dominecfCommented Apr 19, 2016 at 21:13
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$\begingroup$ It was originally thought that the "spin" came from the particle literally spinning, and since it was charged, creating magnetic dipole like a current loop would. The definition then conforms to the classical one. en.wikipedia.org/wiki/Magnetic_moment#Integral_representation $\endgroup$– ConifoldCommented Apr 19, 2016 at 21:55
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1 Answer
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This is simply how the gyromagnetic ratio is defined. Two particles with the same spin may have very different magnetic moments. For example, the electron and the proton have the same spin, but the electron magnetic moment is 638 times larger than the proton magnetic moment. The difference is because the proton is much heavier than the electron and has internal structure. (The magnetic moments of simple point particles are inversely proportional to their mass, while the magnetic moment of composite particles depends on the combined orbital and intrinsic magnetic moments of their constituents.)
Note that although the magnitude of the magnetic moment of a point particle depends on more factors than just the magnitude of the spin, the direction of the point particle's magnetic moment must be parallel to the spin. This is because the magnetic moment is a vector with a direction, and spin is the only intrinsic property of a point particle that has a direction.
answered Oct 22, 2022 at 16:26