# Angular momentum in ElectroMagnetic fields(Feynman's Disk Paradox)

## Main Question or Discussion Point

In Griffiths book, "Introduction to Electrodynamics" example 8.4 he calculates the angular momentum density for a set up that is a version of Feynman disk paradox. His answer for the angular momentum points in the z direction. But if we you assume that the r vector has component in the s direction and z direction(I am almost sure this is correct) $\vec{r}$ = s$\hat{s}$+ z$\hat{z}$, then the angular momentum density has both a z component and s component. The s component is not constant. The total angular moment on the other hand has to end up with only z component or the cylinders would tip over. Where is the error in my reasoning?

It seems to me you've made no error. The angular momentum density should in fact have an $\hat{s}$ component for $z \neq 0$. It seems Griffths neglected this. However, there is no xy component of the total angular momentum of EM field; it cancels out in via integration.