Does the Right Hand Rule Determine Current Direction Without Acceleration?

[Ry122]

Just need to know if current goes from x to y or y to x.
using right hand rule with my thumb pointing towards y and my fingers pointing down (in direction of flux lines) and my palm pointing in direction of force which is straight into the magnet indicates current is in the direction of my thumb.
Is that correct?
Also, since f=m x a and the solenoid is being moved in at a constant speed (no acceleration) that means there should be no force.
Does this mean the right hand rule can't be used in this situation?

 

[CaptainQuaser]

magnetic fields are not linear in all space from a horse shoe magnet. So it will react to the gradient, or the change in flux.
Trying to understand your drawing.
If that is not a horseshoe magnet, but two parallel plates, ignoring edge effects,
well
$\bigtriangledown \times E = -\frac{\delta B}{\delta t}$ so you need a moving magnetic field.
Maybe just explain your problem better, and set up the motion and geometry properly.