  We present a simple and complete classification of static solutions in the
Einstein-Maxwell system with a massless scalar field in arbitrary $n(\ge 3)$
dimensions. We consider spacetimes which correspond to a warped product $M^2
\times K^{n-2}$, where $K^{n-2}$ is a $(n-2)$-dimensional Einstein space. The
scalar field is assumed to depend only on the radial coordinate and the
electromagnetic field is purely electric. Suitable Ans\"atze enable us to
integrate the field equations in a general form and express the solutions in
terms of elementary functions. The classification with a non-constant real
scalar field consists of nine solutions for $n\ge 4$ and three solutions for
$n=3$. A complete geometric analysis of the solutions is presented and the
global mass and electric charge are determined for asymptotically flat
configurations. There are two remarkable features for the solutions with $n\ge
4$: (i) Unlike the case with a vanishing electromagnetic field or constant
scalar field, asymptotically flat solution is not unique, and (ii) The
solutions can asymptotically approach the Bertotti-Robinson spacetime depending
on the integrations constants. In accordance with the no-hair theorem, none of
the solutions are endowed of a Killing horizon.
