A cube of side 2a, centered at the origin and with the x, y, andz axes perpendicular to the faces of the cube, carries a frozen-inpolarization of P = czzˆ, where c is a constant. Note that themagnitude of P is not constant – it is a function of z.

(a) Find the total bound charge inside the cube, and the totalbound charge on each surface of the cube. The sum of all chargesshould add up to zero.

(b) Let E1 be electric field just inside the cube near the point(x, y, z) = (0, 0, a), and let E2 be the electric field justoutside the cube near the same point. Find E2 ? E1.