Point charges +4q, −q and +4q are kept on the X-axis at points x = 0, x = a and x = 2a respectively. Then ___ ?

Point charges +4q, −q and +4q are kept on the X-axis at points x = 0, x = a and x = 2a respectively. Then ___ ? 

(a) only −q is in stable equilibrium

(b) none of the charges is in equilibrium

(c) all the charges are in unstable equilibrium

(d) all the charges are in stable equilibrium

[NEET 1988]

Answer : (c) all the charges are in unstable equilibrium

Coulomb's Law is given by: \[ F = \frac{k \cdot |q_1 q_2|}{r^2} \]

Force between charges \( +4q \) and \( -q \), separated by a distance \( a \):

\[ F_2 = \frac{k \cdot (4q)(q)}{a^2} \]

Force between charges \( +4q \) and \( +4q \), separated by a distance \( 2a \):

\[ F_2 = \frac{k \cdot (4q)(4q)}{(2a)^2} \]

Concept: to be understood here is when the forces are balanced we say it is in equilibrium. So -q and +4q are in equilibrium. 

However -q is not in stable equilibrium because notice that as we make a small disturbance to -q the net force will make it to go towards one direction and will not bring it back to its original position. So it is in unstable equilibrium.