Question

# Three charges (two of same nature) are arranged on a straight line are in equilibrium. This nature of equilibrium is

A
stable
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B
unstable
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C
neutral
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D
Any of the above
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Solution

## The correct option is B unstableFBD of the charges, if charge (−Q3) is slightly displaced to right. Here, F1 is electrostatic force between charges Q2 & Q3 F2 is electrostatic force between charges Q1 & Q3 F3 is electrostatic force between charges Q2 & Q1 F1=kQ2Q3(r2−Δr)2>F ........(1) F2=kQ1Q3(r2+Δr)2<F ........(2) F3=kQ2Q1(r1+r2)2=F ........(3) From (1),(2) and (3), F1≠F2≠F3 For charge +Q1, →Fnet=→F3−→F2≠0 For charge +Q2, →Fnet=→F1−→F3≠0 For charge +Q3, →Fnet=→F1−→F2≠0 It cannot return to original position. Hence, the charges are in unstable equilibrium.

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