Curie's Law can be derived by considering a substance with noninteracting magnetic moments with angular momentum J. If orbital contributions to the magnetic moment are negligible (a common case), then in what follows J = S. If we apply a magnetic field along what we choose to call the z -axis, the energy levels of each paramagnetic center will experience Zeeman splitting of its energy levels, each with a z -component labeled by M J (or just M S for the spin-only magnetic case). Applying semiclassical Boltzmann statistics, the magnetization of such a substance is n m ¯ ¯ = n ∑ ∑ M J = − − J J μ μ M J e − − E M J / k B T ∑ ∑ M J = − − J J e − − E M J / k B T = n ∑ ∑ M J = − − J J M J g J μ μ B e M J g J μ μ B H / k B T ∑ ∑ M J = − − J J e M J g J μ μ B H / k B T .