  We consider fields in (D>2)-dimensional spacetime, whose potential is r-form
(skew-symmetric tensor of rank r), the field tensor F being its exterior
derivative and the Lagrangian, a function of the quadratic invariant I of this
tensor. It is shown that vector field (r=1) describes electromagnetic field
only for D=4. In particular, for D=3 and the Lagrangean L as any function of
the above-mentioned invariant, the (r=1)-field has energy-momentum tensor
identical with that of a perfect fluid whose equation of state depends on the
choice of L(I).
