Assertion (A) : Curl of any vector is a vector. It gives normal vector which is perpendicular to both the plane and the parent vector. Reason (R) : The value of curl of H can be found by the expression : (Curl H)Normal = \(\lim_{\Delta S\to0}\dfrac{\oint \vec{H}\cdot d\vec{l}}{\Delta S}\) where $\Delta S$ is the planar area and $\overline{\text{dl}}$ is the line element. Select your answer using the codes given below.
Both (A) and (R) are true, but (R) is not the correct explanation of (A).
Let's analyze the Assertion (A) and the Reason (R) separately to determine their truth values and relationship.
Assertion (A): "Curl of any vector is a vector. It gives a normal vector which is perpendicular to both the plane and the parent vector."
- The curl of a vector field is indeed another vector field. It is defined in vector calculus and is used to describe the rotation of a vector field.
- The curl is perpendicular to the surface defined by the vector field and a normal vector to it is indeed part of its properties.
- Thus, the assertion is correct since the curl provides a direction normal to the plane formed by the parent vector components.
Reason (R): "The value of curl of H can be found by the expression: \((\text{Curl H})_{\text{Normal}} = \lim_{\Delta S\to0}\dfrac{\oint \vec{H}\cdot d\vec{l}}{\Delta S}\)"
- This expression is a direct application of Stokes' Theorem from vector calculus. It relates the curl of a vector field to a line integral around a closed loop.
- This definition accurately describes how to compute the curl using the limit of a surface integral, confirming the mathematical approach, so the reason is also correct.
Relation between Assertion (A) and Reason (R):
- While both the assertion and the reason are true, the expression given in the reason is a mathematical formulation used to calculate the curl, not an explanation of why the curl is a vector that is perpendicular to the plane and the parent vector.
- Therefore, although both statements are correct, the reason does not serve as the direct explanation for the assertion, making option 2 the correct choice.
Therefore, the correct option is: Both (A) and (R) are true, but (R) is not the correct explanation of (A).
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