Answer:
For electric field inside cylinder, check image 02 attached
For electric field outside cylinder, check image 03 attached
Explanation:
Let's consider the polarized cylinder as superposition of two cylinders with opposite,equal, uniform charge densities in a way shown in the figure in the "image 01"d attached ;
In general, if we have an object with polarization (P¬) , then we have to take two objects with similar shape to the system, with opposite, equal, and uniform charge densities and then we super-impose these two objects in such a way that the total dipole moment of this superimposed system is equal to the total dipole moment of original system.
Now, we can take the super- imposed system as equivalent to the original system for calculating electric field and potential.
Therefore,
For the electric field inside the cylinder, check the solution in "image 02" i attached
For the electric field outside the cylinder, check, "image 03" i attached.
