(Solved): A metal sphere of radius R is charged to a potential = Vo(@) = ? (5 cos? 6 3 cos 6). V,0) = { ...

A metal sphere of radius R is charged to a potential = Vo(@) = ? (5 cos? 6 – 3 cos 6). V,0) = { (scosºo - 3cose). V V is a constant. In spherical coordinates, the potential outside the sphere is: OV(r,0) = VE P2 (cose), Vir, 9) = V5P,(cose), where Pn (2)P_W) is the n p3 R? n-th order Legendre polynomial. V(r,0) = V P2 (cos ), Vír, 9) = v^P,(cose), where Pn (2)?yW) is the n R? 73 n-th order Legendre polynomial. Ov(r,0) = V. Pz (cose), Vír, O= v^P3(cosø), where Pn (2)P_W) is the n R n-th order Legendre polynomial. V(r, 6) = V** P3 (cose), Vir, 9) = v*P3(cosø), where Pn (2)P_W) is the n R n-th order Legendre polynomial.