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 implies |vec(F)_(AO)|=|vec(F)_(BO)|=(KQq_(0))/a^(2)`
When charge is slightly shifted towards + x axis by a small distance `Deltax`, then.

`|vec(F)_(AO)| lt |vec(F)_(BO)|`
Therefore, the particle will move towards origin (its orifinal 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 & it is unstable equilibrium. Finally, the charge will move to infinity.