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Dieletric Boundary Conditions (Parallel Plate Capacitor)

  1. Oct 11, 2011 #1
    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?)
     

    Attached Files:

  2. jcsd
  3. Oct 12, 2011 #2
    Bump, still looking for some help on this confusion please!
     
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