Magnetic tactile perception systems have received increasing attention owing to their simple wiring framework and large-area sensing capabilities. However, existing systems often rely on data-driven methods, which is challenging to extract appropriate tactile representations, especially in complex interaction scenarios. To address such a challenge, this paper realizes a highly interpretable representation of the system's two-stage conversion process (i.e., from changes in magnetic fields to spatial displacements and subsequently into tactile information) with the magnetic dipole model and dynamic Young's modulus. Furthermore, the proposed representation method is incorporated into a novel spherical-array-based system for multi-dimensional tactile perception. Comprehensive experiments in simulated and real environments are conducted on four systems with various array arrangements. The proposed method can achieve relative errors of 0.54% and 1.75% under normal and tangential deformations, outperforming traditional data-driven approaches. It is envisaged that this study would benefit a wide range of industrial and domestic applications, such as remote surgery, dexterous manipulation, and human-robot interaction.