Charged-Particle Circular Orbits around a Schwarzschild Black Hole with a Finite-Width Equatorial Current Source

We study circular orbits of charged particles around a Schwarzschild black hole threaded by the magnetic field of a smooth finite-width equatorial current distribution. We construct an axis-regular source, retain both algebraic circular-orbit branches, and fix the coupling sign through the distant-loop limit, in which strong positive coupling drives the inner marginally stable orbit toward the horizon. We map orbit existence, radial stability, vertical stability, and bound-orbit status for both coupling signs. For positive coupling, radially stable equatorial orbits may separate into an inner band and a detached outer band, with a radial-instability gap between them. For negative coupling, the corresponding separation is produced mainly by loss of an admissible positive-angular-momentum orbit. We also identify stable off-equatorial circular-orbit families. Convergence tests and direct integration verify the principal boundaries. A regular current source can therefore reorganize the circular-orbit structure rather than merely shift the Schwarzschild innermost stable orbit.