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Image charge problem

  1. Feb 2, 2016 #1
    I suppose you are all familiar with the standard image charge problem of calculating the electric potential for a point charge above a grounded conducting plane at y=0. In this case you solve the problem using the method of images.
    I have a slightly problem. Rather than having an infinitely thin conducting plane, mine occupies a region 0<y<a, i.e. it must now hold that V(x,y)=0 for 0<y<a.
    Is it still possible to solve this using the image method?
     
  2. jcsd
  3. Feb 2, 2016 #2
    For the area [itex]y> a[/itex] you can use the same image charge at the appropriate point below [itex] y = a [/itex]. For the area [itex] y < a [/itex] you know can add an image charge [itex]-q[/itex] at the same spot as the original charge to cancel out the charge. Thus [itex] V = 0 [/itex] at all the points [itex] y \leq a [/itex]. This is a round about way of saying that the solution is to Laplace's equation is unique and since [itex]V=0[/itex] at the boundaries we know that [itex]V=0[/itex] is the unique solution for the entire area [itex]y \leq a [/itex].
     
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