Conducting rod through a magnetic field

[thereddevils]

There is this conducting rod being moved to the right a constant speed v by a mechanical force F along 2 parallel , smooth, and horizontal conductors in a uniform vertical magnetic field of flux density B.

The question is why is the speed constant although its being moved by a force ,F.

Well let me answer that first :

Since the conducting rod is being moved through a magnetic field , there is a change in the magnetic flux , hence an emf/current is being induced in the conductor. Now , from Fleming's left hand rule , there exist a magnetic force acting in opposite direction as the mechanical force but are of the same magnitude since the rod moves in Constant velocity.

Another thought came to me , since F=Fm , the conducting rod should be in equalibrium and shouldn't be moving so how did it move with constant velocity according to the question?

 

[RoyalCat]

Remember Newton's First and Second Laws:

$$\Sigma \vec F = \frac{d\vec p}{dt}$$

If $$\frac{d\vec p}{dt}=0$$, what does that tell us about the momentum, $$\vec p=m\vec v$$ ? Does it mean that the velocity is 0, or something else?