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Let A and B be solenoids with the same pole facing each other.
Then will their repulsion cause the set up to jump upwards?

Please correct me if I am wrong: Solenoid A exerts a downward force on Solenoid B, which in turn exerts the same force on the ground. Then due to newton's third law, the ground exerts the same force and the whole thing is pushed upwards. If this force is greater than gravity, the set up will jump upwards. The connecting material makes sure the solenoid B is also carried upwards with Solenoid A.

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It depends on how you apply the current. Just applying a jolt of current will propel solenoid A upward, but leave solenoid B stationary on the ground.

Then due to newton's third law, the ground exerts the same force and the whole thing is pushed upwards. If this force is greater than gravity, the set up will jump upwards.

This is not quite correct. The first sentence is correct, but the normal force is exactly equal to gravity plus the magnetic force. The downward force is also gravity plus the magnetic force, so there is no net force on solenoid B.

On the other hand, if you apply a jolt of current to repel the solenoids, and then another jolt in the opposite direction, here's what happens:

  • solenoid A is propelled upward, solenoid B is stationary
  • then, the solenoids are brought together, bringing solenoid A upward

the net result is that the whole setup moves upward.

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  • $\begingroup$ Thank you very much $\endgroup$
    – Sreenandan Balasubramaniam
    Commented Jun 25, 2023 at 5:30
  • $\begingroup$ If I apply a jolt of current in solenoid A and B, then due to repulsion, when solenoid A jumps, won't it pull solenoid B with it because of the connecting material? $\endgroup$
    – Sreenandan Balasubramaniam
    Commented Jun 26, 2023 at 7:07
  • $\begingroup$ It could. I didn't realize that's what you meant by "connecting material". If the connecting material is rigid (like steel), holding the solenoids at a constant distance, the structure will not move when current is applied. If it is string, then solenoid A will move up and the string will become taut, pulling solenoid B upward. Once solenoid B leaves the ground, the only force to consider is gravity because one solenoid can't be pulled up without the other being pulled down. $\endgroup$
    – Jacob Stuligross
    Commented Jun 27, 2023 at 15:07
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If the structure is not in equilibrium (e.g., if, initially, it was in equilibrium, and then current was created in the solenoids), then yes, I think the structure can jump upwards. This seems similar to two bodies connected by a spring.

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