# the conservation of the Electric displacement vector

Good day everyone!

Consider that we have the following capacitor ( look at the image bellow) that is partially filled with 2 dielectrics with a relative electric constant of er1 and er2, and we have the charges +Q and -Q on the two plates of the capacitor, the question is : 1).calculate the electric field inside the capacitor 2) calculate the charge distribution of the induced charges on the surface S1 and S2. For the first question I have no issue in finding the results by myself but the solution of the book stated something I couldn't understand the book said :*****the Electric vecor displacement D is perpendicular to the plates of the capacitor and to the surfaces S1 and S2 , and since the normal component of the vector D is conserved in the interface between the two condensators, we can conclude that the vector D has the same value everywhere in the capacitor ***** 2). I have an issue regarding the computation of the polarization I know that D= ϵ0*E+P and P=ϵ0*(er1-1)E, for me, the polarization depends only of the initial electric field generated by the free charges, but in the solution of the exercices they used the following formula: P1=ϵ0*(er1-1)E1 and P2=ϵ0(er2-1)*E2 with E1 and E2 are the net electric field inside the two dielectrics

Best regards