Near the plane surface of a uniform isotropic dielectric with permittivity ε the electric field strength in vacuum is equal to E0, the vector E0 forming an angle θ 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 E through a sphere of radius R with centre located at the surface of the dielectric; (b) the circulation of the vector D around the closed path Γ of length l (see Fig. 3.11) whose plane is perpendicular to the surface of the dielectric and parallel to the vector E0.
Solution:
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