This question is about a system involving a horizontal row of length L of equally spaced pivotable magnets, each with a pole at either end. These magnets will often be referred to as units.
So each unit when rotated causes it's neighbours to rotate in the opposite direction to itself.
When the first unit is quickly rotated 1/4 of a turn and fixed in place rotationally, each will likely turn less than the previous at first, taking longer to complete the full 1/4 of a turn. They will all eventually rotate the full 1/4 as the far end of the line is still not fixed.
Turning the first magnet will require energy. For a line of 1000, while this will be more energy than that for a line of for example 2, it will be less than 1000 times the energy required for a line of 1. This is because:
Momentum means that every unit doesn't need to be rotated the full distance to turn the first unit, it is not as if they are connected together by rods, the first can be turned all the way before the others have had time to rotate much at all.
More distant magnets contribute less force, so most units are contributing very little force to the first unit directly. Another way to think about this is that the line of separated magnets forms a compound magnet that will result in more force than each component magnet has individually, but not as much as 1000 times more, for example if metal becomes attached to an end it will take less than 1000 times the force of an individual magnet to remove.
Coils around each unit slow rotation but produce N electricity after 1/4 of a turn, however long the 1/4 turn takes.
The amount of electricity produced appears to be L * N, for an input power that is increment by a diminishing amount for the growth of L, an example of this sort of growth could be sqrt(L).
Question: This has the potential not to add up energy wise for long lines, what's going on?