Magnetoacoustic tomography with magnetic induction (MAT-MI) is a multiphysics imaging technique that combines electrical impedance imaging with ultrasound imaging. In order to study the influence of parameters on the source of MAT-MI, such as radius and permeability of magnetic nanoparticle clusters, the paper is divided into the following stages. Firstly, this paper analyzes the electromagnetic and acoustic properties of MAT-MI after adding magnetic nanoparticles. Secondly, to determine suitable simulation conditions, a two-dimensional model is constructed. Thirdly, use the finite element method to solve physical processes of electromagnetic field and acoustic field under conditions of different magnetic nanoparticle clusters' radii and permeabilities, then obtain the magnetic flux density image. Consequently, make the qualitative and quantitative analysis according to the theory and simulation results. The results show that magnetic nanoparticle clusters interact with each other and distort the magnetic field to different degrees; its radius increases with the degree of flux density distortion around it, so does its permeability and magnetoacoustic signal intensity. The research results can play a guiding role in the parameter selection of magnetic nanoparticle clusters in practical applications to a certain extent.