A small solenoid (radius rₐ ) is inside a larger solenoid (radius r₆ > rₐ ). They are coaxial with nₐ and n₆ turns per unit length, respectively. The solenoids carry the same current, but in opposite directions. Let r be the radial distance from the common axis of the solenoids. If the magnetic field inside the inner solenoid (r < rₐ) is to be in the opposite direction as the field between the solenoids (rₐ < r < r₆) , but have half the magnitude, determine the required ratio n₆/nₐ .