# Is there something similar to the Magnus effect for electromagnetism?

Is there something similar to the Magnus effect for electromagnetism? Would a spinning particle generate a centripetal force moving through something like a circular accelerator? And how would you calculate this?

• Is the particle charged or with E&M moments ? Apr 17 '18 at 15:52
• @qmechanic In the theoretical experiment it would be, I forgot to account for that Apr 17 '18 at 16:53

Electron spin contributes to the centrifugal force on an electron.

Compare the wave function of the hydrogen atom for the Klein-Gordon and the Dirac equation. The KG energy values are

$E_{nl} = \frac{m}{\sqrt{1+[\alpha^2/(n-\delta_l)^2]}}$

with $\delta_l=l+\frac{1}{2}$. The Dirac eigenvalues are obtained by replacing $l\rightarrow j\pm \frac{1}{2}$. See QFT, Itzykson&Zuber, Ch. 2.3.

The reason is that the radial equation in these cases contains the centrifugal potential $\frac{L^2-\alpha^2}{r^2}$ (KG) and $\frac{J^2\alpha^2}{r^2}$ (Dirac). This clearly proves that electron spin like orbital angular momentum exhibits a centrifugal force.

There is a relativistic effect that is similar. If you have an object with a magnetic dipole moment (say a magnet if you want) that is moving straight through the air and encounters an inhomogeneous electric field perpendicular to its motion, then the object will bend its trajectory. Note that is an ELECTRIC field modifying the trajectory of a particle with a MAGNETIC property. The key of the effect is the relative motion. Due to special relativity a moving magnetic moment becomes sort of a electric dipole moment. The magnetic dipole moment may come from neutral electric currents inside the material or intrinsic magnetism.

This effect is a key mechanism to understand the fine structure of hydrogen and spin Hall effect in solids. In such cases, the particle with magnetic moment is an electron with an intrinsic angular momentum AKA spin, some people like to point out an analogy with the Magnus effect.

The Magnus force in electromagnetism is given by $$(4\pi c/\mu_0\omega)\,\vec{B}\times\vec{A}$$.

• What is wrong with my answer? Please give a detailed scientific answer. Jan 20 '19 at 11:00