  We obtain a purely local characterisation that singles out the
Majumdar-Papapetrou class, the near-horizon Bertotti-Robinson geometry and the
Reissner-Nordstr\"om exterior solution, together with its plane and hyperbolic
counterparts, among the static electrovacuum spacetimes. These five classes are
found to form the whole set of static Einstein-Maxwell fields without sources
and conformally flat space of orbits, this is, the conformastat electrovacuum
spacetimes. The main part of the proof consists in showing that a functional
relationship between the gravitational and electromagnetic potentials must
always exist. The classification procedure provides also an improved
characterisation of Majumdar-Papapetrou, by only requiring a conformally flat
space of orbits with a vanishing Ricci scalar of the usual conveniently
rescaled 3-metric. A simple global consideration allows us to state that the
asymptotically flat subset of the Majumdar-Papapetrou class and the
Reissner-Nordstr\"om exterior solution are the only asymptotically flat
conformastat electrovacuum spacetimes.
