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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.

An electron in the ground state of hydrogen atom is revolving in anticlock – wise direction in a circular orbit of radius R. 
  1. Obtain an expression for the orbital magnetic dipole moment of the electron.
  2. 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. 

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Grade:upto college level

1 Answers

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
9 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
askIITians Faculty

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