A superconducting sphere (radius R) placed in a uniform magnetic field B spontaneously generates currents on its surface which produce a dipole magnetic field. The field is equivalent to that produced by a point dipole at the center of the sphere with magnetic moment m = −(2π/μ₀)R³B. Suppose such a sphere (mass · M) begins at infinity with speed ν₀ and moves toward a solenoid along the symmetry axis of the latter. The field deep inside the solenoid has magnitude B_S. What is the minimum value of v₀ such that the sphere will pass through the solenoid (as opposed to reflecting back)? Assume that R

-||- 2R O- W HO Solenoid