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Question

Two positive and equal charges are fixed at certain distance. A third charge (small) is placed in between the line joining of the two charges and it experiences zero net force due to the other two.

A
The equilibrium is always stable
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B
The equilibrium is stable if small charge is positive and is displaced along the line joining two charges.
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C
The equilibrium is not stable
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D
The equilibrium is stable if small charge is negative and is displaced along the line joining two charges.
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Solution

The correct option is B The equilibrium is stable if small charge is positive and is displaced along the line joining two charges.

At equilibrium, the forces F1 and F2 are equal.

So, to check the nature of equilibrium, let us displace the particle slightly towards right from the equilibrium position. Let, the particle is diplaced by x.


Now, from the coulomb's law,

F1=KQq(r2+x)2

F2=KQq(r2x)2

Since, F2>F1 so, Fnet is towards mean point so its a stable equilibrium if positive charge is placed.

If negative charge q is placed between the charges and is displaced slightly towards right , the net force on it will be away from origin i.e. towards point 2 and the particle will not return to its equilibrium position , hence unstable equilibrium.

Hence, option (a) is correct answer.

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