A spherical shell of radius R carries a uniform surface charge 0 on the northern hemisphere and a uniform surface charge 0 on the southern hemisphere Find the potential inside and outside the sphere, calculating the coefficients explicitly up to A 6 and B 6 ...

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A spherical shell of radius R carries a uniform surface charge 0 on the northern hemisphere

Question:

A spherical shell of radius R carries a uniform surface charge σ₀ on the "northern" hemisphere and a uniform surface charge – σ₀ on the "southern" hemisphere. Find the potential inside and outside the sphere, calculating the coefficients explicitly up to A₆ and B₆.