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Particle confinement criteria for velocity space particle loss are used to calculate the radial and axial electric potential profiles in field-reversed configurations (FRC’s). Assuming Vlasov equilibrium distribution functions for both electrons and ions, the density profile and the potential profile are calculated self-consistently. With rest Maxwellian distribution functions for both species and the Hill’s vortex magnetic configuration, a radial electric field of about 0–70 V/cm and an axial electric field of about 0–4 V/cm, depending on positions, have been found for a typical set of experimental parameters: electron temperature Te=100 eV, ion temperature Ti=200 eV, magnetic field B0=5500 G, separatrix radius rs=12 cm, and elongation factor k=5. The corresponding density profile has behavior similar to profiles observed in the experiments. Cases using rigid-rotor distribution functions with different rigid rotating frequencies are also studied. [ABSTRACT FROM AUTHOR]