Magnetic force on open circuit? Let's say we have a straight horizontal wire and we let it drop inside a magnetic field which will be parallel to the ground(coming out of the screen). Charges inside the wire feel a force due to their movement inside the magnetic field .
Let's say the field is coming out of the screen. Positive charges gather on the left and negative on the right. If we had a loop I would have no trouble with this but during the charges' movement do we consider that we have a current? Therefore leading to a magnetic force opposing the bar's drop or not? 
 A: 
So I'll have to ask again, does this ever stop? Is equilibrium ever
  reached?

Prompted by the comments to reexamine the question, I now better understand the question.
Essentially, this is the canonical rod moving in a perpendicular magnetic field extended to the case that there is a constant external applied force.
Clearly, unless there is an oppositely directed magnetic force that cancels the applied force, the rod will accelerate.
But an accelerated rod implies an increasing magnetic force (on charge) parallel to the rod.
Further, if the mobile charge is moving parallel to the rod (an electric current), there is a magnetic force against the external applied force.
What then is equilibrium (the stationary case)?
As user Farcher points out in the comments, the work done by the external can go into the potential energy of the separated charge but it can also go into the kinetic energy of the rod.
(to be continued... it's late now)

You're correct that there is a current but it is a transient current.
As the mobile charge redistributes due to the magnetic force, another force develops - the electric force due to the field from the redistributed charge.
Charge moves just until the electric force and magnetic force on mobile charge cancel out.
