Consider the following situation.
There is a metallic strip situated in an homogeneous electric field. The lines of the electric field go from left to right, so the free electron in the metallic strip are attracted to the left side of the strip. There is a force acting on the free moving electrons of the metal due to the external electric field, F = qE. This force is only capable to move the electrons inside the metallic strip, NOT THE ENTIRE METALLIC STRIP (remember, the electric field is homogeneous).
Now consider this other situation.
There is no electric field anymore, but instead there is a homogeneous magnetic field perpendicular the the sheet of paper. The lines of the magnetic field go from above to below, as it is shown in the picture. There is also an electric current flowing in the metallic strip, the electron move from up to down, as it is shown. Due to the Lorentz force acting on the free electrons of the metallic strip (F = -evB, where v is the electron drift speed), there is an electron buildup on the left side of the strip, just like in the previous situation. This is known as the Hall Effect. But unlike in the previous situation, it is empirically known that THERE IS A FORCE ACTING ON THE ENTIRE STRIP, so the strip would move leftwards.
The question is simple, can you explain why?
Remember, the Lorentz Force should act only on the moving free electrons, not on the ionic lattice of the metallic strip.