  Frame dragging (Lense-Thirring effect) is generally associated with rotating
astrophysical objects. However, it can also be generated by electromagnetic
fields if electric and magnetic fields are simultaneously present. In most
models of astrophysical objects, macroscopic charge neutrality is assumed and
the entire electromagnetic field is characterized in terms of a magnetic dipole
component. Hence, the purely electromagnetic contribution to the frame dragging
vanishes. However, strange stars may posses independent electric dipole and
neutron stars independent electric quadrupole moments that may lead to the
presence of purely electromagnetic contributions to the frame dragging.
Moreover, recent observations have shown that in stars with strong
electromagnetic fields, the magnetic quadrupole may have a significant
contribution to the dynamics of stellar processes. As an attempt to
characterized and quantify the effect of electromagnetic frame-dragging in this
kind of astrophysical objects, an analytic solution to the Einstein-Maxwell
equations is constructed here on the basis that the electromagnetic field is
generated by the combination of arbitrary magnetic and electric dipoles plus
arbitrary magnetic and electric quadrupole moments. The effect of each
multipole contribution on the vorticity scalar and the Poynting vector is
described in detail. Corrections on important quantities such the innermost
stable circular orbit (ISCO) and the epyciclic frequencies are also considered.
