Understanding the Equilibrium of Positively and Negatively Charged Beads

AI Thread Summary
The discussion centers on the equilibrium of a third charged bead positioned between two fixed positively charged beads, 3q and q. The equilibrium position is determined by the balance of forces, where a positive charge can achieve stability through equal repulsion from both fixed charges. In contrast, placing a negative charge between the two positive charges leads to instability, as any deviation would result in an increasing attractive force pulling the negative charge toward one of the positive charges. Therefore, while both charge types can theoretically be positioned between the beads, only a positive charge maintains stability at equilibrium. The key takeaway is that stability in this context is defined by the nature of the forces acting on the charge when slightly displaced.
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Homework Statement


Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x=d. A third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? What type of charge makes makes it stable?


Homework Equations


F= Ke(q1q2)/r^2


The Attempt at a Solution


I got the answer right, but for the second part of the question, the answer booklet said that a positive charge makes this particular situation stable, but I do not get why a negative charge can't also make the situation stable?
 
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what's ur interpretation of 'stable'?
:)
 
That it is possible to place either a positive or a negative charge between the other two positive charges.

the actual value of the unknown charge cancels out of the equation, but I am not sure why a negative charge can not be placed somewhere between the two positive charges.
 
If you take the negative charge between the two charges, the equilibrium position is achieved due to the equal force of attraction. A slight deviation from this position will increase the force of attraction due to one charge then the other and charge will move towards that charge. But in the case of positive charge the equilibrium is achieved due to the equal repulsive force. A slight deviation from this position will push back the charge to the equilibrium position.
 

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