For power electronics systems, the switching transient is critical for efficient and reliable energy conversion. While the electromagnetic (EM) field simulation is instrumental in analyzing switching transients, the simulation is complicated due to the voltage and current's complex distribution and their rapid changes. This article proposes a space partition and time domain decoupling method to model and simulate the 3-D fully coupled EM fields on the time domain for the switching transient, specifically simulating a SiC MOSFET turn-off transient. The space is partitioned into four modules based on different dominant feature in different materials, enhancing the model's numerical stability. Then the time domain decoupling strategy implements staged solving from independent modules to the fully coupled model, effectively coping with the challenges caused by complex coupling relations. We design the spatial fast-changing EM field measurement experiment to validate the model and method's accuracy. The proposed model reveals EM field dynamics during the transient and holds promise for facilitating practical power electronics design, such as the design of EM compatibility (EMC).