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An electron in the ground state of hydrogen atom is revolving in anticlock – wise direction in a circular orbit of radius R.  Obtain an expression for the orbital magnetic dipole moment of the electron. The atom is placed in a uniform magnetic induction 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.

Apoorva Arora IIT Roorkee
7 years ago
1. The electron performs uniform circular motion with period of revolution T. If R is the radius of the orbit, v is the orbital velocity, then,
$T=\frac{2\pi R}{v}$
current =$I=\frac{e}{T}=\frac{ev}{2\pi R}$
magnetic moment is given by M= current X Area
$M=IA=\frac{ev}{2\pi R}\times \pi R^{2}=evR/2$
multiplying and dividing by mass
$M=\frac{eL}{2m}$
1. The revolving electron forms a dipole with a dipole moment derived above, so, the torque acting on a dipole due to a magnetic field is given by$\tau =M\times B=MBsin30^{0}$.
Thanks and Regards
Apoorva Arora
IIT Roorkee