The tangential component of the electric field at the surface of a conductor is zero due to the nature of electrostatics. In electrostatics, conduction electrons within the conductor can move freely, and any tangential electric field would cause these electrons to flow, resulting in an electric current. This contradicts the static condition required for electrostatics. The normal component of the electric field can be non-zero, but if the external electric field exceeds a certain strength, it can free electrons, again leading to current flow and leaving the realm of electrostatics.
PREREQUISITESStudents of physics, electrical engineers, and anyone interested in the principles of electrostatics and electric fields in conductors.
Thank Tou very much for your answer ! That was i was thinking about.vanhees71 said:I think you talk about electrostatics. Then indeed the electric field has a potential and the tangent component of it must vanish, because by definition a conductor consists of a material containing charges (usually electrons, at least for metals) that can move quasi freely within the material. This means that if there where a component of the electric field tangential to the surface of a conductor these conduction electrons would be set into motion due to the electric force in that direction, and you'd have an electric current flowing, but then you are out of the realm of electrostatics. The normal component of the electric field can be non-zero, because the conduction electrons are bound to the conductor. Of course, if you make the external electric field too strong you can free those electrons overcoming the binding energy, but then you also leave the realm of electrostatics, because again an electric current would flow.