In the present article, we investigate the biomechanical response of a fiber reinforced solid matrix (soft tissue) saturated with an electrically conducting fluid. A constant magnetic field was exposed to the binary mixture of fluid and deformable porous solid. The governing mechanism of multiphasic deformation was based on the loading imposed at the rigid bony interface. The fluid flow through the cartilage network depends upon the rate of applied compression and strain-dependent permeability of the solid matrix. The components of the mixture were intrinsically incompressible; however, in the derivation of governing dynamics, the visco-elastic behavior of the solid and an interstitial fluid was developed. The continuum mixture theory was employed in modeling solid deformation and local fluid pressure. We incorporated strain-dependent permeability in the governing equations of binary mixture that was found in an early experimental study. The governing non-linear coupled system of partial differential equations was developed for the solid deformation and fluid pressure in the presence of Lorentz forces. In the case of strain-dependent permeability, a numerical solution is computed using the method of lines (MOL), whereas, the exact solution is provided when permeability is kept constant. Graphical results highlight the influence of various physical parameters on both solid displacement and fluid pressure.