Electricity and magnetism/Electrostatics/Electrostatics of conductive materials

A material is conductive when it contains electrical charges that are free to move. In metals, these charges are the conduction electrons. In semiconductors, they can also be holes, absences of electrons that move in a sea of electrons. In ionic solutions like salt water, the mobile electrical charges are positive and negative ions. Inside a conducting material, the electrostatic field is always zero. Proof: if the field was not zero, the moving charges would be subject to electric forces which would move them, and the field would not be static. On the other hand, electric charges can accumulate on the surface of conductive materials. If we place a metallic object near electric charges, its conduction electrons move to exactly compensate for the electric field imposed from the outside to the inside of the metal. The sum of the two fields, the one imposed from the outside and the one imposed by the electrons which have accumulated on the surface, is always equal to zero inside the metal: File:Condutor-electric-field-compensation.svg On the outer side of the surface of a conductive material, the electric field is perpendicular to the surface. Proof: if the component of the electric field parallel to the surface was not zero, the surface charges would move to cancel it. If the surface charge density is positive, the surface electric field is directed outward from the conductive material. If it is negative, it is directed inward. Proof: if it were the opposite, the electrical forces would push the mobile charges inside the material. The electric field exerts a force on the surface electric charges but cannot move them, because they cannot move out of the material. On the surface of a conductive material, the electric field is where is the surface charge density. The proof is given from Gauss' theorem, in the chapter on Maxwell's equations. Electric charges always move in a direction that tends to cancel out the cause of their movement. Two equal and opposite electric charges produce exactly zero electric field if they are exactly superimposed. When they attract each other, they move in a direction which tends to cancel the electric field which is the cause of their movement. When the terminals of a capacitor are connected with a metal wire, the conduction electrons are subjected to electrical forces, imposed by the charges on the capacitor plates, which move them in the direction of discharge, not in the direction of an increase in charge.