🌀 Equipotential surfaces — E ⟂ surface, E = −dV/dr

Around the charge, join up all the points at one chosen potential and you get an equipotential surface — here the two teal rings. The electric field (brown arrows) is ALWAYS perpendicular to such a surface and points from high to low potential. The size of the field is set by how fast V changes with distance: E = −dV/dr. Squeeze the two shells together (smaller Δr) and the same drop ΔV happens over a shorter distance — so the field gets stronger. Slide q and the spacing Δr.