Not only the fact that you do induce a voltage along the length of the tether-- think about the dynamics induced by the air currents. Anyone who has taken an introductory physics course knows that driven strings exhibit some pretty complex dynamics. It's entirely likely that you couldn't stabilize the tether, that some sort of instability would take hold and snap the damn thing. Incidentally, this is similar to the problems prohibiting viable tokamaks. You start out with what seems like a reasonable stable electron distribution (that is, reasonably close to an equilibrium solution), but small perturbations tend to grow pretty quickly and before you know it you've collided with the chamber wall.