  The unipolar induction DC circuit model, originally developed by Goldreich &
Lynden-Bell for the Jupiter-Io system, has been applied to different types of
binary systems in recent years. We show that there exists an upper limit to the
magnetic interaction torque and energy dissipation rate in such model. This
arises because when the resistance of the circuit is too small, the large
current flow severely twists the magnetic flux tube connecting the two binary
components, leading to breakdown of the circuit. Applying this limit, we find
that in coalescing neutron star binaries, magnetic interactions produce
negligible correction to the phase evolution of the gravitational waveform,
even for magnetar-like field strengths. However, energy dissipation in the
binary magnetosphere may still give rise to electromagnetic radiation prior to
the final merger. For ultra-compact white dwarf binaries, we find that DC
circuit does not provide adequate energy dissipation to explain the observed
X-ray luminosities of several sources. For exoplanetary systems containing
close-in Jupiters or super-Earths, magnetic torque and dissipation are
negligible, except possibly during the early T Tauri phase, when the stellar
magnetic field is stronger than 10^3G.
