Problem 3.83

Under certain conditions the polarization of an infinite uncharged dielectric plate takes the form \(\mathbf{P}=\mathbf{P}_ {0}\left(1-x^{2} / d^{2}\right),\) where \(\mathbf{P}_ {0}\) is a vector perpendicular to the plate, \(x\) is the distance from the middle of the plate, \(d\) is its half-thickness. Find the strength E of the electric field inside the plate and the potential difference between its surfaces.