To solve the question, we need to analyze the assertion (A) and the reason (R) provided:
**Assertion (A):** The equilibrium of a charged particle under the action of electrostatic force alone can never be stable.
**Reason (R):** Coulombian force is an action-reaction pair.
### Step-by-Step Solution:
1. **Understanding Equilibrium:**
- Equilibrium occurs when the net force acting on a charged particle is zero. For a charged particle in an electric field, this means that the electrostatic forces acting on it must balance out.
2. **Types of Equilibrium:**
- There are two types of equilibrium: stable and unstable. In stable equilibrium, if the particle is displaced slightly, it experiences a restoring force that pushes it back to its original position. In unstable equilibrium, any slight displacement results in a force that pushes it further away from the original position.
3. **Electrostatic Force and Stability:**
- Consider a positive charge placed in an electric field created by another charge. If the positive charge is at a point of equilibrium, any small displacement will result in a force that moves it away from that point. This is because the electrostatic force on a positive charge is always directed away from other positive charges and towards negative charges.
4. **Mathematical Analysis:**
- If we take a point charge \( +Q \) in a field created by another charge, the force acting on it due to electrostatic interaction can be described by Coulomb's law. The force will always act in the direction of the electric field, which means that if the charge is displaced, it will not return to its original position, indicating that the equilibrium is unstable.
5. **Gauss's Law Consideration:**
- By applying Gauss's law, we can analyze the electric field around the charge. The total electric flux through a closed surface surrounding the charge is proportional to the enclosed charge. If the charge is displaced, the flux changes, indicating that the net electric field changes, further confirming the instability of the equilibrium.
6. **Conclusion on Assertion (A):**
- Therefore, the assertion that the equilibrium of a charged particle under the action of electrostatic force alone can never be stable is correct.
7. **Analyzing the Reason (R):**
- The reason states that Coulombian force is an action-reaction pair. While this is true (as per Newton's third law), it does not provide a direct explanation for why the equilibrium is unstable. The action-reaction pair concept explains the interaction between two charges but does not relate to the stability of equilibrium for a single charge.
8. **Final Evaluation:**
- The assertion is correct, but the reason provided does not correctly explain the assertion. Thus, the correct conclusion is that statement A is true, statement R is true, but R is not the correct explanation for A.
### Final Answer:
- **Assertion (A) is true.**
- **Reason (R) is true, but it is not the correct explanation for A.**
