Divergence, Curl, Solenoidal, and Irrotational Fields
Curriculum and historical examination lineage for Divergence, Curl, Solenoidal, and Irrotational Fields under Unit 2 (Vector Calculus) of Advanced Calculus and Complex Analysis (21MAB102T) at SRMIST.
Historical appearance distribution across SRMIST Formative Tests (CT1, CT2) and University End Semester examinations.
Factual marks weightage of questions asked on this topic in historical examinations.
Question templates that recur across multiple examination cycles with similar conceptual stems.
“a. Find \(a, b, c\) so that the vector \(\vec{F} = (x+2y+az)\vec{i} + (bx-3y-z)\vec{j} +...”
“The unit vector normal to the surface \(x^2 + y^2 - z^2 = 1\) at \((1,1,1)\) is (A) \((\vec{i} +...”
“If \(\phi\) is a scalar point function then \(\operatorname{curl}(\operatorname{grad} \phi)\) is...”
“If the value of \(\int \limits_A^B \vec{F} \cdot d\vec{r}\) does not depend on the curve C but only...”
“If \(\vec{u}\) and \(\vec{v}\) are irrotational then \(\vec{u} \times \vec{v}\) is”
Representative historical questions extracted directly from SRMIST examination papers.
If \(\phi\) is a scalar point function then \(\operatorname{curl}(\operatorname{grad} \phi)\) is (A) Solenoidal (B) Irrotational (C) Constant (D) 0
If the value of \(\int \limits_A^B \vec{F} \cdot d\vec{r}\) does not depend on the curve C but only on terminal points A and B then \(\vec{F}\) is called (A) Solenoidal vector (B)...
a. Find \(a, b, c\) so that the vector \(\vec{F} = (x+2y+az)\vec{i} + (bx-3y-z)\vec{j} + (4x+cy+2z)\vec{k}\) is irrotational. --- OR --- 22.b. Show that \(\vec{F} = (2xy +...
If \(\vec{u}\) and \(\vec{v}\) are irrotational then \(\vec{u} \times \vec{v}\) is
Answer the following subquestions. (i) Find the directional derivative of \(\phi = x^2yz + 4xz^2 + xyz\) at \((1,2,3)\) in the direction of \(2\vec{i} + \vec{j} - \vec{k}\). (ii)...
Examinations where questions for Divergence, Curl, Solenoidal, and Irrotational Fields have appeared.
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