Question

Two point charges $+q$ and $+q$ are fixed at $(a,0,0)$ and $(-a,0,0)$. A third point charge $-q$ is at origin. State whether its equilibrium is stable, unstable or neutral if it is slightly displaced along $y-$ axis.

• A. Stable
• B. Unstable
• C. Neutral
• D. Data insufficient

Answer 1

The correct option is A Stable

Here, two point charges $+q$ and $+q$ are fixed at $(a,0,0)$ and $(-a,0,0)$ and a third point charge $q$ is at origin. Thus they form a stable equilibrium, since both the positive charges are separated by equal distance from $-q$ charge, the forces due to both $+q$ charges will be equal and balance to each other.
Now, if the charge $-q$ is displaced along y-axis, the forces between charges will change. The horizontal component of the forces will balance each other while the vertical components will add each other and act downward which brings $-q$ in equilibrium. Hence, the charges will in equilibrium for vertical displacement.