Electrical Conductivity

Inside perfect conductors, the electric field is zero. However, for practical conductors, applied electric fields lead to electron flow, causing current.

In the theory of metallic conduction, the resulting current density is proportional to the applied electric field. The proportionality constant is called the electrical conductivity. It is an intrinsic property of the material.

The current through the cross-sectional area is related to the applied electric field. The relationship between the electric field and the potential difference across the conductor's length is then used to relate the current and the potential difference.

The proportionality constant, called the resistance, is inversely proportional to the area and directly proportional to the length, which are both geometric factors. It is directly proportional to the inverse conductivity, called resistivity, which is another intrinsic property of the material.

This relationship is called Ohm's law. It is equivalent to the relationship between the current density and the applied electric field.