  We present a general study about the relation between the vorticity tensor
and the Poynting vector of the electromagnetic field for axially symmetric
stationary electrovacuum metrics. The obtained expressions allow to understand
the role of the Poynting vector in the dragging of inertial frames. The
particular case of the rotating massive charged magnetic dipole is analyzed in
detail. In addition, the electric and magnetic parts of the Weyl tensor are
calculated and the link between the later and the vorticity is established.
Then we show that, in the vacuum case, the necessary and sufficient condition
for the vanishing of the magnetic part is that the spacetime be static.
