1. Electric Potential from Field Suppose we have in some region of space an electric field E = A(x + y)i + Axj, where A > 0 is a constant. (a) Show that V X E = 0, as must be true for any electrostatic field (according to Faraday's law, which we'll study later this semester). (b) Use Gauss's law in differential form, V.E = p/co, to find the charge density p as a function of position in this region of space. (c) Find the electric potential V(x, y), setting the reference at the origin (V (0, 0) = 0). Verify that E = -VV is satisfied