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.