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A dielectric hemisphere

  1. Sep 20, 2012 #1
    1. The problem statement, all variables and given/known data
    we put a dielectric hemishphere with radius (a) and dielectric coeeficient(k) on an infinite conducting plane.the system(hemsiphere and the plane) are in a constant electric field E0.
    find the surface charge distrubution on the plane as a function of (r).
    and explain what happens?
    2. Relevant equations
    E in =1/k E (in a dielectric E weakens)
    maxwell equations
    e0E=surface charge(charge per area)
    3. The attempt at a solution
    for the case k=1 there wont be any charge on the plane(I think)
    also I tried to think what actually happens?will there be any charge inside the hemisphere?
    and these are (I think) the solutions:
    }{r})^2&space;\;&space;\;&space;\;&space;\;&space;r&space;\geq&space;a&space;\end{matrix}\right..gif
     
    Last edited by a moderator: Apr 17, 2017
  2. jcsd
  3. Sep 22, 2012 #2
    anyone??
     
  4. Sep 22, 2012 #3

    SammyS

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    What coordinate is r ?

    There is a charge on the plane, if the electric field is perpendicular to the plane.

    Use Gauss's Law.

     
  5. Sep 22, 2012 #4

    TSny

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    Shouldn't k = 1 correspond to a vacuum (i.e., no hemisphere present)? Then the field should just equal Eo everywhere.

    I don't know your background, but you can solve this problem as a boundary value problem for the electric potential. Then use the potential to get the field at the surface of the plane, and hence the charge density.

    You can also relate this problem to the problem of a dielectric sphere placed in an external uniform field with no conducting plane.
     
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