Can a Positive Charge be in Stable Equilibrium in the Center of a Square According to Earnshaw's Theorem?

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SUMMARY

The discussion centers on the application of Earnshaw's Theorem in the context of electrostatics, specifically regarding a positive charge placed at the center of a square formed by four other charges. While the positive charge appears to be in equilibrium, it is not in stable equilibrium, as any slight displacement will not result in a return to the center. This conclusion aligns with Earnshaw's Theorem, which states that no particle can achieve stable equilibrium under the influence of electrostatic forces alone.

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  • Understanding of Earnshaw's Theorem
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  • Concept of equilibrium in physics
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we have got four charges placed at the ends of a square. if we palce a positive charge in the center, it appeares to be in stable equillibrium; yet earnshaw's theorem(that no particle can be in stable equillibrium if it is under the action of electrostatic forces only) holds. Why is that?
 
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Earnshaw's theorem

The charge at the center of the square is in equilibrium, yes. But it is not in stable equilibrium. Stable equilibrium means that if you move the charge slightly in any direction, then it should return to the center. In this case, as in every other case involving electrostatic forces only, if you move the charge, from the center, it will not return. Check that out.
 

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