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

Inside an infinitely long circular cylinder charged uniformly with volume density P ther is a circular cylindrical cavity. The distance between the axis of the cylinder and the cavity is equal to a. Find the electric field strenght E inside the cavity. The permittivity us assumed to be equal to unity.

If a linear isotropic dielectric is placed in an electric field of strength E, then the polarization P is

A long round cylinderical made of uniform dielectric is placed in a uniform electric field of strength E_(0) . The axis of the cylinder is perpendicular to vector E_(0) . The axis of the cylinder is perpendiucular to vector E_(0) . Under these conditions the dielectrics becomes polarized unifromly. making use of the result obtained in the foregoing probem, find the electric field strength E is the cylinder and the polarization P of the distance whose permittivity is equal to epsilon .

Explain, reduction of electric field due to polarization of a dielectric:

Inside a indinitely long circular cylinder cavity. The distance between the axes of the cylinder and the cavity is equal to a . Find the electric field strength E inside the cavity. The permittivity is assumed to eb equal to unity.

A long round dielectric cyclinder is polarized so that teh vector P = alpha r , where alpha is a positive constant and r is the distance from the axis. Find the space density rho' of bound chagres as a function of distance r from the axis.