Question

An infinitely long round dielectric cylinder is polarized uniformly and statically, the polarization P being perpendicular to the axis of the cylinder. Find the electric field strength E inside the dielectric.

Answer 1

This is to be handled by the same trick as in Q.96. We have effectively a two-dimensional situation. For a uniform cylinder full of charge with charge density ρ₀ (charge per unit volume), the electric field E at an inside point is along the (cylindrical) radius vector and equal to, 

Therefore the polarized cylinder can be thought of as two equal and opposite charge distributions displaced with respect to each other

(direction of electric dipole moment vector being from the negative charge to positive charge .)