Illustration Electric field at the conductive surface

A conducting surface (e.g. of a metallic conductor) with free-moving surface charges (electrons). In addition, a electric field vector \( \boldsymbol{E} \) is drawn in at a point on the surface pointing in arbitrary direction.

This field vector was split into the perpendicular component \( \boldsymbol{E}_{\perp} \) and a parallel component \( \boldsymbol{E}_{||} \). However, the perpendicular component disappears because the surface charges move along the surface until \( \boldsymbol{E}_{||} = 0\). Only the perpendicular field component \( \boldsymbol{E}_{\perp} \) remains. So field lines always come out perpendicularly from the conducting surfaces!