To understand the effect a magnetic field produces on the distortion free energy density, a small region of local nematic order \mathbf{\hat{n}} is often considered in which \chi_\perp and \chi_\parallel is the magnetic susceptibility perpendicular and parallel to \mathbf{\hat{n}}. The value \Delta\chi\equiv\chi_\parallel-\chi_\perp=N, where N is the number of mesogens per unit volume. The work per unit volume done by the field is then given by:
