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A cube of side 2a, centered at the origin and with the x, y, and z...

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

(a) Find the total bound charge inside the cube, and the total bound charge on each surface of the cube. The sum of all charges should 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 just outside the cube near the same point. Find E2 − E1.

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