  As one step towards a systematic modeling of the electromagnetic (EM)
emission from an inspiralling black hole binary we consider a simple scenario
in which the binary moves in a uniform magnetic field anchored to a distant
circumbinary disc. We study this system by solving the Einstein-Maxwell
equations in which the EM fields are chosen with astrophysically consistent
strengths. We consider binaries with spins aligned or anti-aligned with the
orbital angular momentum and study the dependence of gravitational and EM
signals with these spin configurations. Overall we find that the EM radiation
in the lowest l=2, m=2 multipole accurately reflects the gravitational one,
with identical phase evolutions and amplitudes that differ only by a scaling
factor. We also compute the efficiency of the energy emission in EM waves and
find that it is given by E^rad_EM/M ~ 10^-15 (M/10^8 M_Sun)^2 (B/10^4 G)^2,
hence 13 orders of magnitude smaller than the gravitational energy for
realistic magnetic fields. The corresponding luminosity is much smaller than
the accretion luminosity if the system is accreting at near the Eddington rate.
Most importantly, this EM emission is at frequencies of 10^-4 (10^8 M_Sun/M)
Hz, well outside those accessible to astronomical radio observations. As a
result, it is unlikely that the EM emission discussed here can be detected
directly and simultaneously with the gravitational-wave one. However, indirect
processes, driven by changes in the EM fields behavior could yield observable
events. In particular if the accretion rate of the circumbinary disc is small
and sufficiently stable over the timescale of the final inspiral, then the EM
emission may be observable indirectly as it will alter the accretion rate
through the magnetic torques exerted by the distorted magnetic field lines.
