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This is checked the simplest by looking at extreme values. If the rings coincide or h=0 and thus alfa<0 the dumbbell will clearly be pulled into the xy-plane. In the other extreme very far away the rings will of course pull the ring upwards into the z-direction and the dumbbell will align with the z-axis. In between of those there will be no preferred direction, this is the case of alfa = 0.
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