$A$ donut-shaped permanent magnet (magnetization parallel to the axis) can slide frictionlessly on a vertical rod. Treat the magnets as dipoles with mass $m_d$ and dipole moment $M$. When we put two back-to-back magnets on the rod,the upper one will float. At what height $z$ does it float?

• A
  ${\left[ {\frac{{2{\mu _0}{M^2}}}{{3\pi {m_d}g}}} \right]^{1/4}}$
• B
  ${\left[ {\frac{{6{\mu _0}{M^2}}}{{\pi {m_d}g}}} \right]^{1/4}}$
• C
  ${\left[ {\frac{{3{\mu _0}{M^2}}}{{2\pi {m_d}g}}} \right]^{1/4}}$
• D
  ${\left[ {\frac{{{\mu _0}{M^2}}}{{6\pi {m_d}g}}} \right]^{1/4}}$