For both molecules and periodic solids, ionic dynamical charge tensors
-measuring the coupling of electric fields to ionic displacements-are
known to obey a dynamical neutrality condition. This condition forces
their sum to vanish over the whole finite system, or over the crystal
cell, respectively. We extend this sum rule to the nontrivial case of
the surface of a semi-infinite solid and show that, in the case of a p
olar surface of an insulator, the surface ions cannot have the same dy
namical charges as in the bulk. The sum rule is demonstrated through c
alculations for a couple of SiC surfaces.