A. When the slider P of the sliding rheostat moves to the left, the resistance in the connected circuit becomes smaller, the current becomes larger, the magnetism of the energized solenoid is enhanced, and the magnetic flux passing through the coils A and B becomes larger. According to Lenz's law, the increase of magnetic flux will be hindered, so the ampere force generated by two rings tends to shrink to prevent the magnetic flux from increasing, so the ampere force generated is in the same plane with the rings, so it will not swing from side to side, so A is wrong and B is correct.

C, as can be seen from the above, Ampere force makes it tend to shrink, so it will not affect the tension of the thin thread, so C is wrong.

D, because the direction of the magnetic field passing through the two rings is opposite, and the direction of the induced current is opposite according to Lenz's law, D is wrong;

So choose: B.