Let us consider an electron revolving around in a circle of radius with a velocity .

Time period of the electrons orbit is

Current due to the motion of the electron,

Current is in the opposite direction since the electron is negatively charged.

Magnetic moment,

where is the area enclosed by the current loop

Magnetic moment of electron,

(Using (i))

or or

mass ofelectron

or

or orbital angular momentum

Since the angular momentum is

given by the right-hand rule with respect to the velocity and the current in the opposite direction. Hence, the negative sign shows that the two quantities and are in opposite direction