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Homework Help: Electric field enhancement near a surface bump

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Well I got a question regarding the electric field. So let's say an electric field E exists between two parallel plates. There is a hemispherical bump on one of the plates with radius of r, so how to calculate the electric field enhancement?

    Thanks guys.
  2. jcsd
  3. Mar 25, 2012 #2

    rude man

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    Homework Helper
    Gold Member

    If h is the distance between plates, then far away from the hump, V = Eh. At the tip of the hump, the average electric field has to be V/(h-r).

    Away from the tip, you have to determine the path of least distance s between the spot on the hump and the flat plate. The boundary conditions are that the E field must be perpendicular to the hump surface at the hump surface, and to and at the bottom plate. This could be a problem in the calculus of variations. Once you have determined this distance the average E field is again V/s.
  4. Dec 27, 2012 #3
    You have to expand the potential using the orthogonal special functions under your symmetry, at each region, and match the boundary condition for dielectric displacements. Actually there is a paper about this problem: http://www.sciencedirect.com/science/article/pii/003810988190034X
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