- Fully relativistic magnetohydrodynamic (MHD) invariants are used to generalize the force-free equation derived by Michel (1973) and Scharlemann and Wagoner (1973). The version derived here includes general relativistic effects and differential rotation of the compact object to which the field lines are anchored. The effects of forces perpendicular to the magnetic surfaces, such as the inertial forces of a collimated radio jet, can be included at a heuristic level. The equation is solved for simplified, jetlike geometries, and the solutions extend through the boundary of the jet. They explicitly describe the path of the return current to the compact object, and whether the jet is truly self-confined or whether confinement is merely inertial or due to the ambient environment. When the jet is much wider than the light cylinder of the compact object, a self-confined beam has an electrostatic charge density that changes sign somewhere within it, and the material at the boundary of the jet is found to be sealed to the jet by electrostatic attraction to the inner parts. Electrostatic confinement may make an important contribution to the confinement of relativistic jets.