ULR.....I'm not sure I follow,.... you said,..."as the coil approaches the magnet it repels, and attracts when it leaves" ,.....but during the approach power is produced in the coil ,making it an electromagnet ,but of opposite polarity of the mag itself????If this is right than they would be equal??....artv
1) As the coil approaches or retreats from the magnet, it cuts through the magnet's field.
2) Cutting through the field induces a force on the charge carriers in the wire, amounting to an induced voltage "in series with" the other electrical characteristics of the coil (mainly inductance and resistance).
3) If there is a load connected to the coil, the voltage forces a current to flow.
4a) The flowing current delivers energy to the load and to the stray resistance of the coil itself.
4b) The flowing current also produces an additional magnetic field around the coil.
5) The magnetic field from the coil fights the motion of the coil through the magnet's field. If approaching it matches the polarity of the magnet and they repel, if retreating it is flipped from the polarity of the magnet and they attract.
6) The attraction/repulsion of the coil vs. the magnet produces a physical force that fights the motion of the coil with respect to the magnet. The effect is analogous to fluid friction.
7) The mechanical work done by the driving force moving the coil against this electromagnetic fighting of its motion provides the energy which is dissipated in the load and the coil's resistance.
There is no "balancing" of the mag field from the coil with respect to the mag field of the magnet. The faster you push the coil, the higher the current in it, the stronger the coil's field, the harder it fights against being moved, the more power it takes to push it, and the more power delivered to the load and the coil resistance.
There IS a "balancing" of (an equality between) the mechanical work done on the coil and the electrical power delivered to the load, the coil's resistance, and any other parasitic electrical losses. This is how conservation of energy shows up in this situation.
Make sense now?