Problem 1: Potentials and an infinite sheet (25 points) Consider a problem similar in spirit to Griffiths Example 10.2 but instead of an infinite straight wire, we have a neutral infinite sheet which lies is the xy-plane. The surface current K(t) = 0 for t≤0, but at t = 0, suddenly the surface current turns on, so it is a constant Ko in the +x-direction, instantly, and everywhere in this plane. There is no charge density anywhere. (a) Find the (retarded) scalar and vector potentials everywhere in space. In computing your answer, note that √√22]. This will be essential in the parts below. (b) Find the Ę and B fields at a distance z above (or below) the xy-plane. Sketch or draw these fields, and describe them in words. Briefly, comment on them. (Does your answer makes sense, is it e.g. what you would have expected from phys 3310? Part of the answer is a little surprising!) (c) The answer to Part (b) is really an "outgoing plane wave". Show and convince us that this is the case. What direction is the wave propagating? At what speed? (d) Show explicitly that B is not continuous at the (z = 0) xy-plane, but that it satisfies the appropriate boundary condition there. Also, show explicitly that Ẽ also satisfies the appropriate boundary condition at the (z = 0) xy-plane.