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.