The potential on the surface of a sphere (radius R) is given by . (Assume , as usual. Also, assume there is no charge inside or outside, it's ALL on the surface!) i) Find the potential inside and outside this sphere. ii) Find the charge density on the sphere.

Explanation:

The potential on the surface of the sphere is V = V₀cos(2θ) . The potential inside the sphere is the same at all points , which is equal to V as above .

The potential outside the  sphere will decrease with  distance from the center . by the relation V = Q/4πε₀r  ,  where Q is the charge on the surface and r is the distance from the center of the sphere .

Thus the potential decreases inversely proportional to the distance from center of the sphere .

( ii ) The charge density means charge per unit area  . Thus σ = Q/4πε₀r²

Thus σ = V/r

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