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Image method in dielectrics

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data
    The question is attached.

    2. Relevant equations

    3. The attempt at a solution
    I understand that the question would return to a typical conductor problem when ε2 >> ε1 so for the quadrant one, I placed image charges of q_1 at (d1 , 0 , -d2), -q1 at (-d1 , 0 , -d2) and another q1 at (-d1 , 0 , d2) with q1 = (ε1 - ε2)*q/(ε1 + ε2). When I applies the boundary conditions, I find that the image charges for quadrant two is q - q_1 at (d1 , 0 , d2), -q1 at (-d1 , 0 , -d2) and q1 at (-d1 , 0 , d2), for quadrant four is q - q_1 at (d1 , 0 , d2), -q1 at (-d1 , 0 , -d2) and another q1 at (-d1 , 0 , d2). The boundary conditions are well satisfies with these image charges. However, I failed to find image charges for quadrant three satisfying both the continuity of electric field and voltage at the boundaries connecting it with quadrant two and four. I have been working on this question for days and I am really frustrated. Is my attempt of approach is incorrect? Thank you for any help!
     

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    Last edited by a moderator: Nov 6, 2016
  2. jcsd
  3. Nov 6, 2016 #2

    TSny

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    OK
    Are the q1 and -q1 necessary here? Can you satisfy the boundary conditions with just the q - q1 charge?

    When finding the potential or field inside the blue dielectric, I don't think you need to work with each of the three blue quadrants separately. See if you can treat the entire blue dielectric with just one image charge.
     
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