Problem 3.79

Near the plane surface of a uniform isotropic dielectric with permittivity $\varepsilon$ the electric field strength in vacuum is equal to $E_ {0}$, the vector $\mathbf{E}_ {0}$ forming an angle $\theta$ with the normal of the dielectric's surface (Fig. 3.11). Assuming the field to be uniform both inside and outside the dielectric, find: (a) the flux of the vector $\mathbf{E}$ through a sphere of radius $R$ with centre located at the surface of the dielectric: (b) the circulation of the vector $\mathbf{D}$ around the closed path $\Gamma$ of length $l$ (see Fig. 3.11) whose plane is perpendicular to the surface of the dielectric and parallel to the vector $\mathbf{E}_{0}$.