Two-dimensional simulations of various cross-sections under different magnetic field strengths in an electrodeless plasma thruster acceleration part using rotating electric field were conducted. The Particle-In-Cell and Monte Carlo Collision method was used to better understand plasma movement and find the ideal condition for the azimuthal current formation. The findings suggest that raising the voltage amplitude can improve the electric field’s penetration into the plasma, diminish the disparity between the azimuthal current’s maximum and minimum values, and consequently generate a more uniform size and distribution. Peak azimuthal current values are directly proportional to the ac frequency at frequencies above 100 MHz and inversely proportional to the frequency below 100 MHz. A rotating electric field that matches the background magnetic field could be produced by adjusting the phase difference among the two sets of antennas. And then the plasma is accelerated by the effect of E×B to achieve a more favorable azimuthal current. The results also demonstrate that an appropriately sized and distributed azimuthal current benefits more from a magnetic field with a strength between 200 and 1000 G and a value that declines from the cross-section center to its periphery.