Two positive and equal charges are fixed at a certain distance. A thir...
The equilibrium can be stable only if on displacing the small charge slightly in any direction, the forces act on it in such a way so as to bring back the charge to its equilibrium position.
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Two positive and equal charges are fixed at a certain distance. A thir...
Explanation:
The given scenario can be represented by the diagram shown below:
![image.png](attachment:image.png)
Here, two positive charges are fixed at a certain distance and a small charge is placed in between them. The small charge experiences zero net force due to the other two charges.
To determine the stability of the equilibrium, we need to consider the behavior of the small charge if it is displaced slightly from its initial position.
Case 1: Small charge is positive
If the small charge is positive and it is displaced slightly towards either of the fixed positive charges, then it will experience a net force towards the other positive charge. This will cause the small charge to move further away from its initial position, thus making the equilibrium unstable.
Case 2: Small charge is negative
If the small charge is negative and it is displaced slightly towards either of the fixed positive charges, then it will experience a net force towards the other positive charge. This will cause the small charge to move towards its initial position, thus restoring the equilibrium. Similarly, if the small charge is displaced slightly towards the other side, it will again experience a net force towards its initial position, thus making the equilibrium stable.
Therefore, the equilibrium is stable only if the small charge is negative.
Conclusion:
Hence, option D is the correct answer as the equilibrium is not stable if the small charge is positive and it is stable only if the small charge is negative.