A very long cylinder of radius R is made of a polarized dielectric. The polarization vector P = a s where the quantity a is a positive constant and s...

A very long cylinder of radius R is made of a polarized dielectric.

The polarization vector P = a s where the quantity a is a positive constant and s is the radial vector to the cylinder axis. The cylinder rotates round its axis with an angular velocity ω.

(a) Find the electric field E at radius s both inside and outside the cylinder.

(b) Find the magnetic field B at radius s both inside and outside the cylinder, and the direction of B.