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Larmor Precession : Behavior of magnetic Dipole in External magnetic field

Hello friends welcome once again on our blog. In our last post we’ve discussed Pauli’s Exclusion Principle. In this post we are going to discuss Larmor Precession which is another important topic in Atomic Physics.

Note for Reader’s :- the bold letters (e.g. B ) represents vector B.

An electron moving around the nucleus of an atom is equivalent to a magnetic dipole. 

Hence when an ayřtom is placed in external magnetic field, the electron orbit precessesabout the field direction as axis.The precession is called Larmor’s Precession.
Let vector is the external magnetic field and is the orbital angular momentum of the electron. 
Let θ be the angle between and B
The orbital dipole moment  μι of electron is given by :

The torque τ on electron produces a change dL in angular momentum in a time dt. The change dL is perpendicular to L.

Hence the angular momentum remains constant in magnitude but its direction changes.
Therefore traces a cone around such that the angle between them is constant. This is the precession of and hence the electron orbit around B.

Fig 1. Larmor Precession 

If  ω be the angular velocity of precession, then precesses through an angle ωdt in time dt. From fig.1.
 Since, angle = arc/radius

Thus, the angular velocity of Larmor’s precession is equal to product of the magnitude of magnetic field, and the ratio of magnetic moment to magnitude of angular momentum.

It is independent of orientation angle…….. lies between normal (L) and field direction (B) 

Importance : This theorem is of considerable importance in atomic structure as it enables an easy calculations of energy levels in presence pf external magnetic field. 

This is Larmor’s Precession. You can ask any question related to this post in comment section. 

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