[dr_lew]

... The coils share magnetic poles at each end because the current flows into and out of each in the same direction. So, they both act in the same direction, and the motion is reinforced. ...

DOH! I woke up this morning, and I wasn't even really thinking about it, but it suddenly popped into my head that this is wrong. That is because the two coils have opposite handedness as the current orginating from one pole flows in opposite directions around the circle. So I think Cajun is right that the two coils will oppose each other's force on the battery assembly.

I guess the shorter coil will have less resistance and carry more current, in inverse proportion to the lengths, and will overpower the opposing force of the longer coil.

[The Cajun]

Dang it, now you're going to cause me to get a piece of paper and diagram the dang thing out, LOL!

[The Cajun]

If I'm thinking right, some doubt about that, with the coil connected (closed loop), it would appear to me that the long coil's magnet polarity would offer some opposition to the battery "train" movement rather than reinforced it.

And than again, I could be totally off track :)