A circuit breaking electromagnetic system is the actuator and digital controller for a switching device. Its performance can significantly affect operations of the switching device. We propose a dynamic simulation method coupling the electric field and the magnetic field for the circuit breaking electromagnetic system and its drive circuit. The method combines both statistic and dynamic analyses, and differential equations. Finally, we utilize the flux transformer as an example to validate this method and reveal the dynamic characteristics of the drive transformer by changing the parameters of the drive circuit.