Aharonov-Bohm (AB) effect is a very significant phenomenon of quantum mechanics. It demonstrates the significance of electromagnetic potentials (proportional to fluxes) against the electromagnetic fields through the simple paradigm of two electron beams (e-beams). Even though they are both traveling through a null field space, their wave functions are not equal: the difference is in their phases and it is related to the magnetic flux through the area defined by their trajectories. Inspired by this fact, we formulate an inverse problem for the magnetic permeability of a bio-chemical sample positioned in-between two magnets. The data can be taken by measuring the phase difference between the wave functions of two split e-beams with parallel trajectories passing through the samples. The case of only radial dependence of magnetic permeability is fully solved and certain insights are provided for the arbitrary radial/azimuthal distributions.