V x B= 0, where B is the magnetic field (in SI units of Tesla) H is the magnetic intensity (A/m) j is the current density (A/m²) M is the material magnetisation (A/m), which can depend non-linearly on the applied magnetic field (material saturation and hysteresis) x is the magnetic susceptibility (unitless) Ho is the permeability of a vacuum (4л× 10-7 N/A²)

These equations hold true both in a vacuum and in materials. For a permanent magnetic material, the magnetisation M↑ 0; for an electromagnet, the current density is non-zero j↑ 0. Applied magnetic fields pass virtually unchanged through the human body because the magnetic susceptibility of blood and tissue is close to zero (x≈ 10-6-10-4). In contrast, ferromagnetic particles can have magnetic susceptibilities 5-7 orders of magnitude higher (x≈ 20) resulting in strong interactions with magnetic fields. This means magnetic particles can experience magnetic forces, while biological tissues remain unaffected.