Calculation of the electric potential in some simple systems

It is presented an easy and rapid form to calculate the electrical potentia l in two very common cases in electromagnetism; one is due to a volumetric charge distribution and the other is due to a sphere with a potential known in its surface. We show that in order to derive these results it is necess ary that the angular part of the volumetric charge distribution or the pote ntial at the surface of the sphere can be written as a linear combination o f spherical harmonic Y-lm(theta, phi) for a fixed value or l.