See figure attached for problem statement, as well the 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,
\(\hat{n} \cdot \vec{D_{1}}  \hat{n} \cdot \vec{D_{2}} = \rho_{s}\)
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,
\(\rho_{s0}, \rho_{s1}, \rho_{s2}, \rho_{s3}\)
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,
\(\rho_{s0} = \rho_{s3}, \quad \rho_{s1} = \rho_{s2}\)
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?)
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,
\(\hat{n} \cdot \vec{D_{1}}  \hat{n} \cdot \vec{D_{2}} = \rho_{s}\)
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,
\(\rho_{s0}, \rho_{s1}, \rho_{s2}, \rho_{s3}\)
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,
\(\rho_{s0} = \rho_{s3}, \quad \rho_{s1} = \rho_{s2}\)
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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