An electron in the ground state of hydrogen atom is revolving in anticlock-wise direction in a circular orbit of radius `R`.
(i) Obtain an experssion for the orbital magnetic dipole moment of the electron.
(ii) The atom is placed in a uniform magnetic induction `vec(B)` such that the plane - normal of the electron - orbit makes an angle of ` 30^(@)` with the magnetic induction . Find the torque experienced by the orbiting electron.

Answer

(i) `(he)/(4pim)` (ii) `(ehB)/(8pim)`

Explanation

(i) Magnetic moment `=IA=(ehn)/(4 pi m)`
Produced is `n^(th)` orbit
for hydrogen `n=1 implies` Magnetic moment`=(eh)/(4 pi m)`
(ii) `vec(tau)=vec(M)xxvec(B)=(eh)/(4pi m)xxBxxsin 30^(@)=(ehB)/(8 pi m)`