Translational symmetry parallel to a plane
= Translational symmetry parallel to a plane
A scalar field unchanged by every <translation> parallel to a specified <plane> depends only on the coordinate normal to that plane. For <electrostatics> between ideal infinite parallel plates, this reduces <Laplace's equation> to $d^2V/dz^2=0$. Finite plate edges break the exact symmetry and produce <fringing field>.