The dipole will only be stably levitated at points where the energy has a minimum. The energy can only have a minimum at points where the Laplacian of the energy is greater than zero. That is, where ∇ ∇ 2 U = ∂ ∂ 2 U ∂ ∂ x 2 + ∂ ∂ 2 U ∂ ∂ y 2 + ∂ ∂ 2 U ∂ ∂ z 2 > 0.