  We consider an action for an abelian gauge field for which the density is
given by a power of the Maxwell Lagrangian. In d spacetime dimensions this
action is shown to enjoy the conformal invariance if the power is chosen as
d/4. We take advantage of this conformal invariance to derive black hole
solutions electrically charged with a purely radial electric field. Because of
considering power of the Maxwell density, the black hole solutions exist only
for dimensions which are multiples of four. The expression of the electric
field does not depend on the dimension and corresponds to the four-dimensional
Reissner-Nordstrom field. Using the Hamiltonian action we identify the mass and
the electric charge of these black hole solutions.
