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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. enter image description here

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

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I just want to share the answer to my question: for the first point: the book was refering to the boundary conditions of the Electric field for more details this youtube video explain it well https://www.youtube.com/watch?v=YbQJspnPm6Q&t=1015s

for the second part the fomula used comes from the gauss law, and from it we can only use the field that enters the surfaces so E1 not the initial electric field

Thanks!!!

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