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## Homework Statement

*Introduction to Electrodynamics (4th Edition) By J Griffth*Ch.4

Problem 4.18

The space between the plates of a parallel-plate capacitor is filled with two slabs of linear dielectric material. Each slab has thickness a, so the total distance between the plates is 2a. Slab 1 has a dielectric constant of 2, and slab 2 has a dielectric constant of 1.5. The free charge density on the top plate is σ and on the bottom plate −σ.

(a) Find the electric displacement D in each slab

## Homework Equations

$$\epsilon_r = \frac{\epsilon}{\epsilon_0}$$

$$D = \epsilon_r\epsilon_0 E $$

And for parallel plate capacitor.

$$E_{vac} = \frac{\sigma}{\epsilon_0}$$

## The Attempt at a Solution

How do I relate ##E## to ##E_{vac}##? I see in the text when you don't need to worry about boundary condition, $$D = \epsilon_0 E_{vac}$$. But I am not very sure what that means in this setup. There are 3 boundaries in this problem. Solution online and the solution given by my professor to a similar question seem to have$$\epsilon= \epsilon_0 $$ somehow. The link seems trivial(?) so that neither of these solutions explained this.