Consider a particle of charge Q and mass M describing a circle of radius a with angular velocity ω.

The equivalent current is        i = Q x frequency = Qω /2π                    ... (1)

The current generates a magnetic dipole moment
        m = iπa² = Qωa² /2                                ... (2)

Let L be the angular momentum of the same particle in its orbit. The magnitude of L is Mωa² and its direction is given by the right and screw rule. Mass M is always positive and therefore the directions of L and ω are identical. Vectors m and L are parallel when Q is positive.
For a positively charged particle,
            M = Qa² ω/2                                ... (3)

Gyro magnetic ratio g = m/L 1/2Qωa² /Mωa² = Q/2M                            ... (4)

For a negatively charged particle,
            m = -Qa²ω/2                                ... (5)
            g = m/L = Q/2M                                ... (6)
The negative sign indicates that vectors m and L have opposite direction.

For more help in The Gyro magnetic Ratio click the button below to submit your homework assignment.