Question

the magnitude of magnetic moment of an electron e orbiting in a circular orbit of radius r with a speed v is equal to​

Answer 1

The magnitude of magnetic moment of an electron e orbiting in a circular orbit of radius r with a speed v =(evr)/2

Basically when an electrons orbit ,it behaves as a current loop.

The current due to the orbiting electron,

I = q/T = e/T { q = charge,T = time period of the orbiting motion}

The speed of e = v

Radius of orbit = r

so,

T = (2 π r )/v

Therefore I = (e)/(2 π r)/v = ev/2πr

Magnetic moment of a current loop = IA (Area of loop)

Magnetic moment = (evr)/2