Suppose the surface charge density over a sphere of radius R depends on a polar angle as 0 cos , where 0 is a positive constant Show that such a charge distribution can be represented as a result of a small relative shift of two uniformly charged balls of radius R whose charges are equal in magnitu...

We start from two charged spherical balls each of radius R with equal and opposite c ...

Suppose the surface charge density over a sphere of radius R depends on a polar angle as

Question:

Suppose the surface charge density over a sphere of radius R depends on a polar angle θ as σ = σ0 cos θ, where σ0 is a positive constant. Show that such a charge can be represented as a result of a small relative shift of two uniformly charged balls of radius R whose charges are equal in magnitude and opposite in sign. Resorting to this representation, find the electric field strength vector inside the given sphere. Distribution
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