Two equal positive point charges 'Q' are fixed at points B (a, 0) and A(-a, 0). Another test charge `q_(0)` is also placed at O (0, 0). Show that the equilibrium at 'O' is
(i) Stable for displacement along X-axis
(ii) Unstable for displacement along Y-axis.

Explanation

(i)
Initially `vec(F)_(AO) + vec(F)_(BO) = 0 rArr |vec(F)_(AO)| = |vec(F)_(BO)|`
`= (KQq_(0))/(a^(2))`
When charge is slightly shifted towards +x axis by a small distance `Delta x`, then
`|vec(F)_(AO)| lt |vec(F)_(BO)|`

Therefore the particle will move towards origin (its original position) hence the equilibrium is stable.
(ii) When charge is shifted along y axis

After resolving components net force will be along y axis so the particle will not return to its original position so it is unstable equilibrium. Finally the charge will move to infinity.