1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook