Problem 3.249

A long dielectric cylinder of radius $R$ is statically polarized so that at all its points the polarization is equal to $\mathbf{P}=\alpha \mathbf{r},$ where $\alpha$ is a positive constant, and $\mathbf{r}$ is the distance from the axis. The cylinder is set into rotation about its axis with an angular velocity $\omega .$ Find the magnetic induction $\mathbf{B}$ at the centre of the cylinder.