Question Analysis: Assertion-Reasoning type question based on Electrostatics.

Step 1 (Governing Law & Conceptual Definition): [0.5 Mark]

• Assertion (A): A force is defined as conservative if the work done by or against the force in moving a particle between two points is independent of the path taken. For an electrostatic force $\vec{F} = q\vec{E}$, the work done $W$ is given by: $$W = -\int_{A}^{B} \vec{F} \cdot d\vec{l} = q(V_A - V_B)$$ Since the potential difference $(V_A - V_B)$ depends only on the endpoints $A$ and $B$, the electrostatic force is indeed conservative. Thus, Assertion (A) is True.

Step 2 (Step-by-Step Logical Evaluation): [0.25 Mark]

• Reason (R): The work done per unit positive charge between two points is defined as the potential difference $\Delta V = V_B - V_A$. By the property of conservative fields, the line integral of the electric field $\vec{E}$ is path-independent: $$\oint \vec{E} \cdot d\vec{l} = 0$$ The statement in Reason (R) claims that work done depends on the path, which contradicts the fundamental property of conservative fields. Thus, Reason (R) is False.

Step 3 (Final Concluded Answer): [0.25 Mark]

Since Assertion (A) is True but Reason (R) is False, the correct option is:

Answer: Assertion (A) is true, but Reason (R) is false.

💡 EL10 Concept Insight: Think of a conservative force like climbing a mountain; whether you take a steep direct path or a winding zigzag trail, the change in your altitude (potential energy) remains exactly the same because it only depends on where you started and where you finished.