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This is a theoretical physics question, please answer clearly A hollow sphere of radius R has an electric potential V(R, p) = f() on its

This is a theoretical physics question, please answer clearly

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A hollow sphere of radius R has an electric potential V(R, p) = f() on its surface (with / = cos 0 and 0 is the polar angle) where f() and the potential outside the sphere V(r, 0) are +Vo (-1 R) pl+1 1=0 +Vo (1/2 0 and Pi() are the Legendre polynomials. Starting at / = 0, calculate the constatnts Brin turn up to and including By, the first coefficient that is non-zero. Show that the electric field at large distance from the sphere, r >> R, falls off as the fourth power of the radius, E x r-4. Explain why the field does not fall off like a Coulomb field E x r-2 or a dipole field E xx p-3

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