An electron in the ground state of hydrogen atom is removing in unanticlockwise direction in a circle orbit of radius `R`

a. Obtain an expression for the orbital magnetic dipole moment of the electron .
b. The atom is placed in a uniform magnetic indution `bar B` such that the plane normal to the electron orbitmakes an angle of `30^(@)` with the magnetic induction. Find the tarque 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)`