According to the coupling relationship of electromagnetic field and acoustic field when electromagnetic field irradiates low conductivity objects, we carried out a study on the magnetoacoustic effect and thermoacoustic effect in pulsed magnetic excitation. In this paper, we provide the pressure wave equation in pulsed magnetic excitation based on the theory of electromagnetic field and acoustic wave propagation. A 2-dimensional coil carrying current and a circular thin sheet model were constructed to simulate the physical imaging environment. The transient electromagnetic field was simulated using finite element method. Numerical studies were conducted to simulate the pressures excited by magnetoacoustic effect and thermoacoustic effect according to the result of electromagnetic simulation. It was shown that the thermoacoustic effect played a leading role in the low conductivity objects on the microsecond Gauss pulsed magnetic excitation, and thermoacoustic effect and magnetoacoustic effect coexisted on the microsecond Gauss pulsed magnetic field and 0.2 T static magnetic field excitation. This study lays the foundation for the further application of magnetoacoustic tomography with magnetic induction and magnetically mediated thermoacoustic imaging.