1. The problem statement, all variables and given/known data A very long cylinder of liner dielectric materil is placed in an otherwise uniform electric field [tex]E_0[/tex] . Find the resulting field within the cylinder. (the radius is a , the susceptibililty [tex]\chi_e[/tex] and the axis is perpendicular to [tex]E_0[/tex]) 2. Relevant equations 3. The attempt at a solution [tex]V_in(r,\theta)= \sigma(l=0..infinity)A_l*r^l*P_l(cos(\theta)[/tex] should I take the derivative of [tex]V_in[/tex] with respect to r to obtain the field? Not sure why latex isn't display infiinity but l is supposed to range from zero to infinity I also know that [tex]E_0[/tex] = [tex]\lambda/(2*\pi*\epsilon_0*a)[/tex] [tex]P_0=\epsilon_0*\chi_e*E_0[/tex] [tex]P=\epsilon*\chi_e*E[/tex] ; should I plugged [tex]\chi_e=P/(E_0*\epsilon_0)[/tex] into P to get E?