The heating of the electrons in a plasma by radio frequency (rf) fields results in an electron distribution function that can be highly non-Maxwellian. The response of these heated electrons can lead to a substantially larger total potential drop than that obtained by arbitrarily choosing a single-temperature parameter to describe the electron distribution in a traditional Boltzmann approximation. Electromotively driven rf fields can have scale lengths along a static magnetic field line that are much larger than a Debye length and produce electron–sheath interactions that are best described as collisions. Estimates of the floating potential of a plasma that is excited by electromotively driven rf plasma currents parallel to a strong static magnetic field have been made using a Fermi acceleration heating model and linear estimates for the rf fields with plasma. When this non-Maxwellian distribution function is used for estimates of the static potential, the results show that the total potential drop is proportional to the rf oscillation energy and the square root of the ion to electron mass ratio. Numerical solutions to Poisson’s equation are presented for non-Boltzmann electrons. Analytic estimates of parasitic rf power absorption and edge profile modification using a Bohm diffusion model are presented. Estimates for a purely electrostatic heating operator with rf fields that are assumed to scale as the Debye length along static magnetic field lines are also made for comparison with the electromagnetic result.