1. Analyze Statement-1

Electrostatic force is a conservative force. For any conservative force, the work done in moving a particle from point $P$ to point $Q$ depends only on the initial and final positions, not on the path.

Mathematically, $W_{P\to Q} = -\Delta U = U(P)-U(Q)$ so the work is determined only by the potential difference between $P$ and $Q$.

Therefore, Statement-1 is true.

2. Analyze Statement-2

A defining property of a conservative force is that the net work done over any closed path is zero: $\oint \vec{F}\cdot d\vec{r} = 0$

Hence, Statement-2 is true.

3. Check whether Statement-2 explains Statement-1

If the work done over every closed loop is zero, then consider two different paths from $P$ to $Q$, say path 1 and path 2.

Let the work along path 1 be $W_1$ and along path 2 be $W_2$. Traverse from $P$ to $Q$ along path 1 and return from $Q$ to $P$ along path 2. This forms a closed loop.

So, $W_1 + (-W_2) = 0$ which gives $W_1 = W_2$

Thus, the work done from $P$ to $Q$ is independent of path. So Statement-2 is indeed the correct explanation of Statement-1.

4. Evaluate options

• A: Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1. ✅
• B: Incorrect
• C: Incorrect
• D: Incorrect

Therefore, the correct answer is A.