Show that the magnetic moment of an atom is `M = 1/2 eomegar^2` , where e the charge of an electron , `omega` - angular speed of electron and r - the radius of electron orbit.

Explanation

The electrons are revolving round of nucleus of an atom. If .e. is the charge of an electron and T its period of revolution , then
Current `I=e/T=(eomega)/(2pi)`. Since `T=(2pi)/omega, omega` is the angular velocity .
If `A = pir^2` , is the area of the orbit of radius .r. , then magnetic moment of the atom,
`M=IA=(eomega)/(2pi).pir^2=1/2eomegar^2`