Problem 1. As we studied in lectures, one of important vector fields in engineering is the electric field E. In the simplest case, if an electric charge q is located at the origin, it generates a filed at the point r = (x, y, z) as: E (x, y, z ) = ATEO Tr 3' Tr|3' Tr/3 ) y where |r| = Vx2+32 + 22. a) Show that the total flux passing through the surface x2 + y2 + 22 = a2 for arbitrary a > 0 is F =4. Evidently, the total flux is independent of the radius a of the sphere. b) The results in part a confirms that the total flux passing through the surface x2 + 2 + 22=1 and x2+ y2+ 22 =4 is the same. Now, assume that S is a closed smooth surface between these two spheres. S What is the total flux passing through S? Justify your