Problem 3.100

A long round cylinder made of uniform dielectric is placed in a uniform electric field of strength \(\mathbf{E}_ {0} .\) The axis of the cylinder is perpendicular to vector \(\mathbf{E}_{0}\). Under these conditions the dielectric becomes polarized uniformly. Making use of the result obtained in the foregoing problem, find the electric field strength \(\mathbf{E}\) in the cylinder and the polarization \(\mathbf{P}\) of the dielectric whose permittivity is equal to \(\varepsilon\).