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The expression of the gyromagnetic ratio is given by-

$\gamma_e = \frac{ge}{2m_e}\\$

If I substitute the values of the constants $e$ and $m_e$, and take $g\sim2.022$, I get $\gamma_e = 1.76 \times10^{11}$ [SI units]. The units should be $C kg^{-1}$, which converted to magnetic field units should be equal to $T^{-1}s^{-1}$. However, the value from wikipedia is $1.76 \times10^{11}$ [rad/Ts]. I seem to be missing a factor of $2\pi$, which I do not understand.

rahman62
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1 Answers1

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Radians are dimensionless. You’re not missing a $2\pi$. For example, when talking about an angular velocity, you can say “20 radians per second” or just “20 per second”.

G. Smith
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