A conducting solid sphere of radius \( R \) and mass \( M \) carries a charge \( Q \). The sphere is rotating about an axis passing through its center with a uniform angular speed \( \omega \). The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as \( \alpha \, \dfrac{Q}{2M} \). The value of \( \alpha \) is ________.
