Problem:

Consider a 3d rectangular region with dimensions 0<=x<=w,0<=y<=h,0<=z<=L.

Potential is 0 on all surfaces except for the surface on the z=0 plane, where

v(x,y)=(w/2-|x-w/2|)(h/2-|y-h/2|).

Calculate V(x,y,z) assuming no charges or dielectrics are present within the region.

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I tried solving using the separation of variables method and failed miserably. I got V(x,y,z)=0