Problem

Problem

Two positive charges +q+q each are fixed at points (−a,0)(-a, 0) and (a,0)(a, 0). A third charge +Q+Q is placed at origin. Corresponding to small displacement of +Q+Q in the direction mentioned in Column I, match the corresponding equilibrium of Column II.
Column IColumn II
(a) Along positive xx -axis(p) stable equilibrium
(b) Along positive yy -axis(q) unstable equilibrium
(c) Along positive zz -axis(r) neutral equilibrium
(d) Along the line x=yx = y(s) no equilibrium
Intuitive explanation

The key is analyzing the net electrostatic force on +Q+Q after small displacements in each direction. Since all charges are positive, they repel; the question is whether the force pushes +Q+Q back toward origin (stable), away from it (unstable), or stays zero (neutral). By symmetry, displacements along xx experience equal repulsion from both fixed charges that add along that axis, while yy and zz displacements create restoring components. Sketch the force geometry for each direction to determine whether the net force opposes or amplifies the displacement.

Intuitive explanation

The key is analyzing the net electrostatic force on +Q+Q after small displacements in each direction. Since all charges are positive, they repel; the question is whether the force pushes +Q+Q back toward origin (stable), away from it (unstable), or stays zero (neutral). By symmetry, displacements along xx experience equal repulsion from both fixed charges that add along that axis, while yy and zz displacements create restoring components. Sketch the force geometry for each direction to determine whether the net force opposes or amplifies the displacement.

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