Question Detail
Question
Which of the following condition(s) is/are correct about conservative force field, F? i. ∇ × F = 0; ii. ∮ F·dr = 0; iii. F = ∇φ; iv. ∫ F·dr = 0
Correct Answer
Option B is the correct answer.
Detailed Explanation
For a conservative force field: (i) the curl is zero (∇ × F = 0), (ii) the line integral around a closed path is zero (∮ F·dr = 0), and (iii) the force can be expressed as the gradient of a potential (F = -∇φ, not F = ∇φ; the sign may vary but the gradient relation holds). So i and ii are correct. iii is almost correct but usually with a negative sign. iv is incomplete as it doesn't specify closed path. The best answer is i and ii.
Hint
Recall the properties of conservative forces: zero curl, path independence, and zero closed-loop work.