Find Charge q3 for System of Charges in Equilibrium

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SUMMARY

The discussion centers on determining the charge q3 required for equilibrium between two fixed point charges, q1 and q2. According to Coulomb's law, for q3 to achieve equilibrium, it must be positive when placed between q1 and q2, as a negative charge would lead to unstable equilibrium. The options provided indicate that the correct answer is that equilibrium is only possible if q3 is positive. If q1 and q2 are not fixed, the dynamics change, and further analysis is required to ascertain the nature of q3.

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Homework Statement


Two point charges + q1 and + q2 are fixed with a finite distance d between them.It is desired to put a third charge q3 in between these two charges on the line joining them so that the charge q3 is in equilibrium.What has to be the charge on q3 to make this possible/


Homework Equations


Coulomb's law


The Attempt at a Solution


I think the answer is that q3 is positive,since if it is negative,the equilibrium will be iunstable.But what if q1 and q2 are not fixed?Will q3 have to be negative then?
 
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It sounds to me like the problem wants a magnitude of charge, not merely a sign of charge. Also, what's wrong with an unstable equilibrium?
 
Actually,the question was of an objective type,and the options involved only the sign of charge.Here are the four options given:
a.possible only if q3 is positive
b.possible only if q3 is negative
c.possible irrespective of sign of q3
d.not possible at all

So is the correct option c?

What will be answer be if we modify the question so that q1 and q2 are not fixed?
 

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