Two coaxial solenoids of different radii carry current I in the same direction. Let be the magnetic force on the inner solenoid due to the outer one and be the magnetic force on the outer solenoid due to the inner one. Then:
The net force on both the solenoids will be zero.
So, Fnet = F1 + F2 = 0
These two forces also form an action reaction pair as they act on two different bodies.
Hence, they both should be equal.
So, F1 = F2 = 0