  Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric
g, and let T be the electromagnetic energy tensor associated to a 2-form F. In
this paper we characterize this tensor T as the only 2-covariant natural tensor
associated to a lorentzian metric and a 2-form that is independent of the unit
of scale and satisfies certain condition on its divergence. This
characterization is motivated on physical grounds, and can be used to justify
the Einstein-Maxwell field equations. More generally, we characterize in a
similar manner the energy tensor associated to a differential form of arbitrary
order k. Finally, we develop a generalized theory of electromagnetism where
charged particles are not punctual, but of an arbitrary fixed dimension p. In
this theory, the electromagnetic field F is a differential form of order 2+p
and its electromagnetic energy tensor is precisely the energy tensor associated
to F.
