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

To solve the problem, we need to analyze the forces acting on the test charge \( q_0 \) placed at the origin \( O(0, 0) \) due to the two fixed positive charges \( Q \) located at points \( A(-a, 0) \) and \( B(a, 0) \). We will show that the equilibrium at \( O \) is stable for displacements along the X-axis and unstable for displacements along the Y-axis.

### Step-by-Step Solution

#### Part (i): Stability for Displacement Along the X-axis

1. **Identify Forces Acting on \( q_0 \)**:
- The charge \( q_0 \) experiences electrostatic forces due to both charges \( Q \) at points \( A \) and \( B \).
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