1. The problem statement, all variables and given/known data 1. A parallel plate capacitor, with plates of area A, and spacing d, is filled with a non-uniform dielectric, with a permitivity that varies as ε = ε0 + ax where a is a constant, and x is the distance from one plate 2. Relevant equations C = Q/V I'm assuming I'm allowed to assume this is a linear dielectric so P = XeE D = P + E = (1+Xe)E = εE Where P is the polarization vector and Xe is electric susceptibility and D is the electric displacement -grad(P) = ρbound P dot n = σbound Where n is a unit vector normal to the surface ε = ε0(1+χe) 3. The attempt at a solution I am able to solve for Xe and sub it back into the equation for P So P = ax/ε0E And I know that the E from the plates is σfree/ε0 And that C = Q/V and that the sum of the bound charges should be zero because otherwise conservation of charge would be violated so V should be changing. But I am really unsure what to do to figure out the total electric field.