# A point charge near an infinite conducting plane

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?