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

DC Circuit Powered by Orbital Motion: Magnetic Interactions in Compact Object Binaries and Exoplanetary Systems