# Lorentz force in Zeeman effect

I’m reading Zeemans 1897 paper on his discoveries of line splitting.

https://articles.adsabs.harvard.edu/full/1897ApJ.....5..332Z

He cited Lorentz who says that a circular rotating “ion” ( electron presumably) will have a different rotational period between Clockwise and counter clockwise rotation but neglects to explain details of what the force is that causes this different rotational periods observed in Zeeman. In the original 1897 Zeeman paper section 18 on the bottom of page 339 he, Lorentz, only says an “elastic force draws the ion back to its equilibrium” just below 2 equations of his which have +- in them depending on direction of rotation.

One seperate explanation given to me is the rotation of the “ion” is subject to a “confining force”. But I find no clear explanation online of what exactly this “confining force” is. By “confining force” do they mean the q>0 and q<0 in the wiki illustration linked below:

https://en.wikipedia.org/wiki/Lorentz_force#/media/File:Lorentz_force.svg

And is that the same as the Lorentz force on a conductor in a magnetic field? (ie the left hand rule) If so one problem I have with this is that if Lorentz’s “ion” is the electron and is negatively charged then that would only give a rotation in one direction in Zeemans experiment. Seeing as to get observed both directions of rotation and thus two seperate observed frequency lines split from the original spectral line in the experiment one would have to have a positive and negative rotating particle . Not just a neg ion.Yet Zeeman observed both CW & CCW polarisations when the light path was parallel to the magnetic field.How do the two seperate frequency with two oppositely circularly polarised light get explained if the “ion” is always only neg charged?

## 1 Answer

The spin of an electron should not be associated with rotation. It is much more obvious to equate spin and magnetic dipole moment. Because always, when it comes to the deflection of the charged particle (with kinetic energy) in a magnetic field, the external magnetic field and that of the particle interact. The deflection simply does not work any other way. Incidentally, electromagnetic radiation always occurs when particles are deflected.

The Zeeman effect is also about the interaction of the external magnetic field and that of the electrons. As is well known, the emission of EM radiation is modified by an applied magnetic field. In the atom, the previously balanced magnetic moments of the electrons are distorted in relation to each other by the external magnetic field and this changes the respective energy that an electron with spin up or spin down needs to jump to the next energy level or returns from there by emitting the typical frequency.

• Yes interesting answer but mostly about current theory which was not what I was looking for. What I really was trying to find out was what was Lorentz’s (Nobel prize winning)thinking in 1897 re Zeeman effect when he said an applied mag field would create two seperate CCW & CW rotations of the sodium ions at 2 sep frequencies. His quote says this is done by an “elastic” force. Did he mean the Lorentz force? Because if he did it’s not clear how his Lorentz force could make the heated sodium ions rotate CW and CcW at 2 sep frequencies. In 1897 how does a Lorentz force produce these 2 f in ions? Commented Apr 13, 2023 at 16:41