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Homework Help: Dielectric-Dielectric Boundary Conditions Problem

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data
    The problem can be found http://whites.sdsmt.edu/classes/ee382/homework/382Homework4.pdf" [Broken]. It is the first one. Note: The subscript x = 0 is supposed to be y = 0 (the teacher typed it in wrong).

    2. Relevant equations
    [tex]\vec{\boldsymbol{D}}_{2t} = \epsilon_{2}\vec{\boldsymbol{D}}_{1t}/\epsilon_{1}[/tex]

    [tex]\vec{\boldsymbol{D}}_{2n} = \vec{\boldsymbol{D}}_{1n}[/tex] (assuming [tex]\rho_{s} = 0[/tex] because it isn't mentioned)

    [tex]\vec{\boldsymbol{D}}_{2} = \vec{\boldsymbol{D}}_{2t} + \vec{\boldsymbol{D}}_{2n}[/tex]

    3. The attempt at a solution
    [tex]\vec{\boldsymbol{D}}_{2t} = \epsilon_{2}\vec{\boldsymbol{D}}_{1t}/\epsilon_{1} = \epsilon_{2}(\hat{\boldsymbol{a}}_{x}\alpha + \hat{\boldsymbol{a}}_{z}\gamma)/\epsilon_{1}[/tex]

    [tex]\vec{\boldsymbol{D}}_{2n} = \vec{\boldsymbol{D}}_{1n} = \hat{\boldsymbol{a}}_{y}\beta[/tex]

    [tex]\vec{\boldsymbol{D}}_{2} = \vec{\boldsymbol{D}}_{2t} + \vec{\boldsymbol{D}}_{2n} = \epsilon_{2}(\hat{\boldsymbol{a}}_{x}\alpha + \hat{\boldsymbol{a}}_{z}\gamma)/\epsilon_{1} + \hat{\boldsymbol{a}}_{y}\beta[/tex]

    Is this all there is to it, or do I need to do something with the y = 0 stuff? My teacher told me that I'm supposed to evaluate the given vector at y = 0, but since the vector contains no y's, it doesn't make any sense to me. It seems kind of redudant to me, actually. Do you suppose the y = 0 is just telling me where the boundary is located (if I wasn't able to figure it out from the figure)? If someone could cure me of my confusion, that would be great. Thanks.
    Last edited by a moderator: May 4, 2017
  2. jcsd
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