Force acting on a current carrying hollow conductor within a magnetic field It is known that when a current carrying conductor is placed within a magnetic field and current flows perpendicular to the magnetic field, a force is exerted on the conductor. 
In figure 1, a square hollow conductor is shown in which current, I, is flowing perpendicular to the magnetic field, B.  By Flemings left hand rule, the force acts downwards on the whole conductor. 
 
What happens when the same current carrying conductor is subject to a magnetic field generated within? In figure 2, the same hollow square conductor is wrapped with an energized coil and magnetic field is generated within its cross section.  Current is made to flow through the conductor in the same way as figure 1.  Would a perpendicular force be exerted on each of the four sides of the square cross-section?  Could someone please explain this for me? 
 A: 
... when a current carrying conductor is placed within a magnetic field and current flows  perpendicular  non-parallel to the magnetic field, a force is exerted on the conductor.

The reason for the force is the deflection of each moving electron of the current in the direction perpendicular the current and the field.

What happens when the same current carrying conductor is subject to a magnetic field generated within? Would a perpendicular force be exerted on each of the four sides of the square cross-section?

Nice device. Apply the left hand rule to each of the four sides of the hollow conductor and you’ll see that the electrons following a spiral path. The same happens if you take a tube instead of a square hollow conductor. Making the wrap not touching the hollow conductor you get a rotor of an electric motor.
One remark.
Usually all inductive processes are interchangeable. From the three components electric current, magnetic field, force from two of them one get the third. So what happens if one rotate the hollow conductor and apply a current? Since the moving electrons “feel“ a centrifugal force, their spins get aligned and you get the transformer again. In the coil a current will be induced.
