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Homework Help: Boundary between dielectrics

  1. Mar 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Say I have a boundary between two dielectrics then it's easy to show using a gaussian pillarbox that:
    D(1)-D(2)=free surface charge density=s
    where D(1) is the component of the first medium normal to the surface.
    But suppose that there's nothing else apart from two infinite dielectrics with a constant free charge density between then, how would I work out what the actual values of D(1) and D(2) are rather than just the difference?

    3. The attempt at a solution
    It seems reasonable that the D field should be the same on both sides so that D=s/2 but I'm not sure how I'd prove this?

    Any help appreciated.
     
  2. jcsd
  3. Mar 13, 2008 #2
    I'm having a hard time interpreting what you are asking. Could you draw it?
     
  4. Mar 13, 2008 #3
    I think my question was badly worded/ ive probably misused some terminology.

    I suppose my actual qustion is:
    Its obvious from the symmetry that for an uncharged nonconducting non-dielectric that if you put a surface charge density s on it the field above is the same magnitude as the field below: D=s/2.

    But suppose that the material is a dielectric then I'm not sure how you prove what the D field is above the surface (in air) and below the surface (in the dielectric) (under the same condition of the dielectric being infinite with surface charge s and no other free charge anywhere)

    Hope this is a bit clearer, please say if it isn't.
     
  5. Mar 13, 2008 #4
    Oh, well D is going to be the same for both air and the dielectric, but E will be different because E is D/(epsilon) which will change between the two (epsilon_0 for air and dielectric epsilon in the dielectric). Is this what you are asking about?
     
  6. Mar 13, 2008 #5
    That's it.

    Its probably really obvious but how do you know that D has to be the same on both sides of the boundary?
    Thanks
     
  7. Mar 13, 2008 #6
    It comes from the way D is defined. After its whole redefinition then you just get a Gauss's Law for materials which goes as

    [tex]\iint \mathbf{D} \cdot d\mathbf{a} = \sigma_f[/tex]

    and that means that the only thing that you care about is the free charge, which will be the same on both sides.
     
  8. Mar 13, 2008 #7
    Thanks.
     
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