1. Find the eld inside a linear dielectric ball (with relative permittivity 6,.) in an otherwise uniform electric eld E0. This is a problem we solved in class. However, let us pursue a different method by considering the following iterative method: (a) (1 point) First pretend the eld inside the dielectric ball is just the external eld E0. Find the resultant polarization P0 in terms of E0 and 6,. This polarization generates its own electric eld E1 through the induced charges. Find E1 in terms of E0 and Er. (b) (1 point) The polarization induced eld E1 modies the polarization by an amount P1, which further corrects the eld by an amount E2. Find P1 and E2 in terms of E0 and Er. (c) (1 point) Repeating this logic of successive correction ad innitum. Find the resulting eld E0 + E1 + E2 + - ' ' and polarization P0 + P1 + P2 + . .. by summing the series