3.` The surface charge density on a spherical shell of radius R is constant, +σ 0 , on the entire northern hemisphere, and −σ 0 on the entire southern hemisphere. There are no other charges present inside or outside the sphere. (a) Use the method of separation of variables in spherical coordinates to find the electrical potential both inside and outside this sphere. You do not need to work out the expression of the coefficient explicitly. You can express each coefficient in the integral form. (b) Your result in (a) should be the summation of an infinite number of terms. Work out explicitly the first nonzero term, for both V(rR). (c) Using the concept of multipole expansion, explain physically why the first term in your solution to (a) is zero.