Find Charge q3 for System of Charges in Equilibrium

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To achieve equilibrium for charge q3 placed between two fixed positive charges q1 and q2, q3 must also be positive; otherwise, the equilibrium would be unstable. The discussion raises the possibility of q1 and q2 being movable, which could change the required charge on q3. The original question focuses on the sign of q3, with options indicating that it must be positive for equilibrium. The conclusion suggests that the correct answer is option a, as equilibrium is only possible with a positive q3. If q1 and q2 are not fixed, the dynamics of the system would require further analysis to determine the necessary charge on 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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