Let m₁, m₂, and m₃ be three point dipoles.
(a) Find the constraints that must be imposed on the m_α and their positions r_α if the asymptotic magnetic field is octupolar.
(b) Show that one class of solutions places all the dipoles (with suitable magnitudes) on a line (separated by suitable distances) with their moments pointing parallel or anti-parallel to one another. Sketch an example.
(c) Show that another class of solutions has all the dipoles at the corners of a triangle and, if s_α is the length of the side opposite m_α, m₁ : m₂ : m₂ = s₁ : s₂ : s₃.