Chapter 7. ElectrodynamicsThe Electromotive Force
In order to sustain an electric current, a force must be applied to the charges. In most materials, the current density is proportional to the force per unit charge:
The force acting on the charges is in most cases the electromagnetic force. In this case, the current density is equal to:
The approximation used in the last step is correct if the velocity of the charges is small (v << c).