Assertion A: Curl of Electric Field is Zero

Assertion A states that the curl of the electric field ($ \mathbf{E} $) is zero.

For static electric fields (electrostatics), this statement is correct. It can be expressed mathematically as:

$ \nabla \times \mathbf{E} = 0 $

This property arises because electrostatic fields are conservative, meaning they can be derived from a scalar potential ($ \mathbf{E} = -\nabla V $).

Reason R: Line Integral of Electric Field is Zero

Reason R states that the line integral of the electric field around a closed path is zero.

This statement is also correct for electrostatic fields:

$ \oint \mathbf{E} \cdot d\mathbf{l} = 0 $

This implies that the work done by an electrostatic field in moving a charge between two points is path-independent.

Relationship and Explanation Validity

Stokes' Theorem relates the curl of a vector field to its line integral:

$ \oint \mathbf{E} \cdot d\mathbf{l} = \int (\nabla \times \mathbf{E}) \cdot d\mathbf{A} $

Given that $ \nabla \times \mathbf{E} = 0 $ (Assertion A), it directly follows from Stokes' Theorem that $ \oint \mathbf{E} \cdot d\mathbf{l} = 0 $ (Reason R).

The fundamental reason Assertion A is true is the conservative nature of the electrostatic field. Reason R is a consequence or manifestation of this same conservative property, demonstrable via Stokes' Theorem. It is not the primary reason *why* the curl is zero, but rather a related property that holds true because the curl is zero.

Conclusion

Both statements A and R are correct in the context of electrostatics. However, Reason R is a consequence derived from the property stated in Assertion A (or they are equivalent properties). Therefore, R does not serve as the fundamental explanation *for* Assertion A being true.

Thus, the most appropriate choice is that both A and R are correct, but R is NOT the correct explanation of A.