Correct Option: (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Step 1 (Governing Law & Definition): [0.25 Mark]
The electric field produced by static charges is a conservative field. By definition, the work done ($W$) in moving a unit charge ($q$) in a closed loop within a conservative field is given by the line integral of the electric field:
$$W = \oint \vec{E} \cdot d\vec{l}$$Step 2 (Mathematical Working): [0.5 Mark]
Since the electric potential ($V$) is a state function, it depends only on the position of the point. If a charge starts at point $A$ with potential $V_A$ and returns to the same point $A$ after traversing a closed loop, the change in potential ($\Delta V$) is:
$$\Delta V = V_{final} - V_{initial} = V_A - V_A = 0$$The work done ($W$) in moving a charge $q$ is related to the potential difference by:
$$W = q \cdot \Delta V = q \cdot 0 = 0$$Step 3 (Final Concluded Answer): [0.25 Mark]
Because the potential difference between the starting point and the ending point of a closed loop is zero, the total work done in taking a unit charge around the closed loop is zero. Thus, Assertion (A) is true, and Reason (R) correctly explains that the path independence of potential leads to this result.
💡 EL10 Concept Insight: Think of electric potential like the height of a hill; if you hike around a mountain and end up exactly where you started, your total change in height is zero, meaning you didn't gain or lose any "elevation energy" overall.