The general solution for the potential (spherical coordinates with azimuthal symmetry) is: = - Σ [Air² + 1] Pi (cos 0) B₁ pl+1 l=0 V(r, 0) Consider a specific charge density o.(0) = k cos³0, where k is constant, that is glued over the surface of a spherical shell of radius R. Solve for the potential outside the sphere. Hint: Express the surface charge density as a linear combination of the Legendre polynomials.

The general solution for the potential (spherical coordinates with azimuthal symmetry) is: = - Σ [Air² + 1] Pi (cos 0) B₁ pl+1 l=0 V(r, 0) Consider a specific charge density o.(0) = k cos³0, where k is constant, that is glued over the surface of a spherical shell of radius R. Solve for the potential outside the sphere. Hint: Express the surface charge density as a linear combination of the Legendre polynomials.