Question: Which one of the following statements is correct? Electric field due to static charges is (A) conservative and field lines do not form closed loops. (B) conservative and field lines form closed loops. (C) non-conservative and field lines do not form closed loops. (D) non-conservative and field lines form closed loops.
Step 1 (Governing Law & Definition): [0.5 Mark]
An electric field $\vec{E}$ is defined as conservative if the line integral of the field around any closed path is zero:
$$\oint \vec{E} \cdot d\vec{l} = 0$$This property is a direct consequence of the fact that the electrostatic force is a central force and the work done in moving a charge in an electrostatic field is path-independent.
Step 2 (Step-by-Step Deduction): [0.25 Mark]
- Since the electrostatic field is conservative, the potential difference between two points is uniquely defined.
- Electric field lines originate from positive charges and terminate at negative charges (or infinity).
- If field lines formed closed loops, the work done in moving a unit positive charge along the loop would be non-zero, which contradicts the conservative nature of the electrostatic field.
Step 3 (Final Concluded Answer): [0.25 Mark]
The correct statement is (A) conservative and field lines do not form closed loops.
💡 EL10 Concept Insight: Think of a conservative field like a hill; if you walk in a circle and end up back where you started, you haven't gained or lost any height, meaning no net work was done. Because electric field lines always "flow" from high potential to low potential, they can't loop back on themselves without breaking the rules of energy conservation.