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Longer problems (30 pts.) A solid sphere (radius a, centered at the origin) carries a volume charge distribution p(z) Po a. i. Find the dipole contribution to the electric potential at an arbitrary point (x, y = 0, z = 0). ii. If the top half of the sphere rotates about the z-axis with angular velocity woź, and the bottom half of the sphere rotates with angular velocity - wo2, find the dipole contribution to the magnetic field at an arbitrary point on the x axis (x, y =0, z=0). b. (35 pts.) The surface of a hollow sphere (radius a, centered at the origin) is held at a potential of (r = a, 0, y) = Posinecoso. A uniform line charge (charge density 10) extends from (x = 0, y = 0, z = a) to (x = 0, y = 0, z = 3a). Find expressions for the potential outside the sphere. v