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I want to calculate (with Poisson's equation) the electric field in the region containing a point charge near an infinite conducting plane with 0 potential. My textbook uses V(x,y,z)= 0 for every x,y,x of the plane as boundary condition.

However, in resolving Poisson's equation don't we need to use the boundary condition of a surface that encloses the portion of space we are studying? In this case the infinite plane is not a closed surface. Where am i wrong?

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The other boundary condition is that the potential goes to zero at infinity.

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  • $\begingroup$ What are the rules for defining the correct boundary conditions ? I searched by there is nothing clear on the web.... $\endgroup$
    – JDOE
    Commented Nov 18, 2017 at 8:43
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    $\begingroup$ Whenever the charge distribution is localized, the potential at infinity goes to zero. (Or to any constant, if you feel like defining it to be non-zero). $\endgroup$
    – Chris ♦
    Commented Nov 18, 2017 at 9:47
  • $\begingroup$ @JDOE, since the conducting plane (an equipotential surface) extends to infinity and is at zero potential, what other reasonable choice for the potential at infinity is there? $\endgroup$
    – Alfred Centauri
    Commented Nov 18, 2017 at 13:08

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