(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

See figure attached for problem statement, as well the solution.

2. Relevant equations

3. The attempt at a solution

I'm confused as to how he is writing these equations from the boundary conditions.

What I understand as the boundary condition for D is,

[tex]\hat{n} \cdot \vec{D_{1}} - \hat{n} \cdot \vec{D_{2}} = \rho_{s}[/tex]

With the normal vector directed from region 1 to region 2.

With this I only generated 2 equations, as there is only 2 boundarys; one being from d1 to d2 and the other from d2 to d3.

He labels,

[tex]\rho_{s0}, \rho_{s1}, \rho_{s2}, \rho_{s3}[/tex]

I'm confused as to what these surface charge densities pertain to? Is the surface charge density with subscript 0 and 3 the charge on the plates of the capacitor? Are 1 and 2 the surface charge densities on the faces of the dielectric material?

He states by conservation of charge that,

[tex]\rho_{s0} = -\rho_{s3}, \quad \rho_{s1} = -\rho_{s2}[/tex]

This doesn't seem obvious to me at all. Can someone show me how he is drawing such a conclusion? (Is there some math behind it?)

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# Dieletric Boundary Conditions (Parallel Plate Capacitor)

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