An electric field cannot exist within a conductor at equilibrium because the fields from opposite sides cancel each other out, resulting in a net electric field of zero. If the conductor is not at equilibrium, such as when a voltage or current source is applied, the electric field becomes non-zero, allowing charge carriers to move. This movement disrupts equilibrium, indicating that an external force is acting on the charges. The relationship between the electric field and current in this scenario is described by Ohm's law. Understanding these principles is essential for analyzing electrical circuits and conductor behavior.