Method of Images: Grounded Conductors

Hold a charge near a grounded conductor and something has to give: a conductor cannot have any field along its surface, so the charges inside it rearrange until the field meets the metal at a perfect right angle everywhere. Working out that rearrangement looks hard, until you notice a trick. The field in the empty region is exactly the field of the real charge plus a few fictitious image charges placed where the conductor used to be, chosen so the potential is zero on the surface. Those images reproduce the real induced surface charge perfectly and pull the real charge in with a genuine, measurable force. Switch the geometry to see the classic cases from Griffiths: a single image below a grounded plane; three images for a right-angle corner; five for a sixty-degree wedge; and the one image inside a grounded sphere, sitting at the inverse point R squared over d with charge scaled by R over d. The scene shows the field lines bending in to strike the surface head-on and the induced charge shaded along the boundary; flip to reveal image and the conductor vanishes, leaving only the image charges. The diagnostic plots the induced surface charge along the conductor.