ABSTRACT
The electromagnetic field contributes its variables to the action, to the Lagrangian of the whole system of charges and fields. In contrast with the point charges, the field is distributed in space. This invariance of the action must imply a corresponding conservation law. To determine what is conserved, we compute the change in the Lagrangian explicitly. Electric charge is a property carried only by the particles, not by the electromagnetic field. In contrast, the mechanical properties of energy, linear, and angular momentum are attributes of both particles and fields. The time displacement of a complete physical system identifies its total energy. This suggests that time displacement of a part of the system provides energetic information about that portion.
