Magnetic flow and mechanical advantage question

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Hi - I'm a layman with a problem I'd really appreciate some help with. I've been studying tattoo machines and have a question on magnetic flow and mechanical advantage.
For background a tattoo machine is a essentially an electric horseshoe magnet with a bridge across the poles (doorbell switch): two electromagnets vertically mounted on a steel bar (the yoke). At the other end of the magnets there is a bar on a hinge (armature bar) - the fulcrum point is located below the bottom electromagnet. In the neutral state the armature bar is rotated away from the top electromagnet, so that when the electromagnets are activated it pulls the armature bar closed (it lays flat across the tops of the electromagnets). I hope this is clear with the diagram.

So my question is this: Does the direction of magnetic flow make a difference on the force closing the hinge? If so, what would be the correct orientation of magnetic poles for the strongest pull on the armature bar (does the diagram show the correct orientation of poles if it does matter)?

I'm trying to understand this better, but I'm not well versed in physics, etc.
Thanks,
Tom
 

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