Electron dynamics in a beating-electrostatic-wave-powered magnetic null thruster are explored in order to determine a mechanism that allows for electrons to exit the thruster. Electron behavior inside of the region of magnetic field reversal is shown to be different from that of the ions due to the relative difference in characteristic Larmor orbit size compared to the characteristic size of the null. The analysis led to a thruster design criterion stated in terms of the relative sizes of electron and ion Larmor radii. An analytical expression for the fraction of electrons which experience adverse reverse drifting orbits inside the null is derived. Additionally, the expected drift velocity of forward moving electrons within the null region is calculated. A scaling relationship for the rate at which electrons enter the null region through collisional processes is also developed. These three parameters are all shown to be dependent on a single non-dimensional ratio of the electron thermal Larmor radius to the size of the null region.