1. The problem statement, all variables and given/known data It's example 3.8 in the Griffiths book in case someone has it. Basically the problem involves a uncharged metal sphere in a uniform field in the +z direction. Naturally, there will be induced positive charges on top and negative charges at the bottom. The question asks for potential outside the sphere. 2. Relevant equations 3. The attempt at a solution What I don't get is how he deduces that the xy plane is at 0 potential using symmetry, after setting the metal sphere to be 0 potential. What I'm thinking is maybe it's because the E field (even with distortion from induced charges) is perpendicular to the xy plane at all points so moving out in xy-plane causes no change in potential. This satisfy the symmetry. But there could also be an E field with a component pointing inward towards the z-axis. Or one with a component outward from the z-axis. And these latter possibilities would also work but would not give 0 potential from the xy-plane. I need help finding a convincing argument to eliminate these two options. Intuitively, I can see that they violates symmetry of the Coulomb force between positive and negative charges (ie E field acting on a positive charge is same as for negative charge but only in opposite direction) but they are symmetric geometrically.