  We introduce two classes of rotating solutions of Einstein-Maxwell gravity in
$n+1$ dimensions which are asymptotically anti-de Sitter type. They have no
curvature singularity and no horizons. The first class of solutions, which has
a conic singularity yields a spacetime with a longitudinal magnetic field and
$k$ rotation parameters. We show that when one or more of the rotation
parameters are non zero, the spinning brane has a net electric charge that is
proportional to the magnitude of the rotation parameters. The second class of
solutions yields a spacetime with an angular magnetic field and $% \kappa$
boost parameters. We find that the net electric charge of these traveling
branes with one or more nonzero boost parameters is proportional to the
magnitude of the velocity of the brane. We also use the counterterm method
inspired by AdS/CFT correspondence and calculate the conserved quantities of
the solutions. We show that the logarithmic divergencies associated to the Weyl
anomalies and matter field are zero, and the $r$ divergence of the action can
be removed by the counterterm method.
