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A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega$. The ratio of the magnitude of its magnetic moment to that of its angular momentum is
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$\frac{q}{2 m}$
Ratio of magnitudes of magnetic moment and angular momentum of rotating charged particle in an orbit is called its 'Gyromagnetic ratio' its' value is equals to $1 / 2$ of specific charge of the particle.
$\therefore \text { Gyromagnetic ratio }=\frac{M}{L}=\frac{1}{2}\left(\frac{q}{m}\right)$
$\therefore \text { Gyromagnetic ratio }=\frac{M}{L}=\frac{1}{2}\left(\frac{q}{m}\right)$
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