Question

An electron is revolving around a proton in an orbit of radius r with a speed v. Obtain expression for magnetic moment associated with the electron.

Answer 1

Consider an electron moving around a proton anticlockwise as shown in the figure,

Equivalent current,

`I = "Change"/"Time"`

= `e/T`

= `e/((2pir)/v) = (ev)/2pir`

Area of the current loop, A = πr²

Therefore, the orbital magnetic moment (magnetic moment due to orbital motion) of the electron is

`mu_l = IA`

= `(ev)/(2pir) * pir^2`

or `mu_l = (evr)/2`