Question

Two positive charges +q each are fixed at points(-a,0) and (a,0).A third charge +Q +Q is placed at origin.Corresponding to small displacement of +Q in the direction mentioned in column I. Match the corresponding equilibrium of column II :

List 1	List 2
A. Along the positive x-axis	1. stable equilibrium
B. Along the positive y-axis	2. unstable equilibrium
C. Along the positive z-axis	3. neutral equilibrium
D. Along the line $x=y$	4. no equilibrium

• A. A$\to$1, B$\to$2, C$\to$2, D$\to$4
• B. B$\to$1, C$\to$2, D$\to$2, A$\to$4
• C. C$\to$1, D$\to$2, A$\to$2, B$\to$4
• D. D$\to$1, A$\to$2, B$\to$2, C$\to$4

Answer 1

Answer: (A)

A$\to$1, B$\to$2, C$\to$2, D$\to$4

(a) Net force is towards the mean position $x$ = 0, where, $F$ =0 when displaced from this position. Therefore, equilibrium is stable.
(b) Net force is away from the mean position. Therefore, equilibrium is unstable.
(c) Same logic can be applied as was applied in part (b).
(d) Net force is neither towards $X=0$ nor away from $X=0$. Therefore, equilibrium is none of the three.