Two long solenoids are nested on the same axis as in the shown
in the figure below. The inner solenoid has radius R1 and n1 turns
per unit length. The outer solenoid has R2 and n2 turns per
unit length. Each solenoid carries the same current I flowing in
each turn, but in opposite directions. Use Ampere’s law to find the
direction and magnitude of the magnetic field in the following
regions.
(a) 0 < r < R1
(b) R1 < r < R2
(c) R2 < r