Question:
Gauss divergence theorem states the relation between
Gauss divergence theorem states the relation between
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Think of it this way: Green's = Line/Surface; Gauss = Surface/Volume; Stokes = Line/Surface.
Updated On: Jul 3, 2026
- surface integral and volume integral
- a line integral and a surface integral
- line integral and a volume integral
- gradient of a function and its surface integral
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Gauss Divergence Theorem is a fundamental theorem in vector calculus relating the flux through a surface to the divergence within the volume.
Step 2: Meaning
It is mathematically expressed as $\iint_{S} F \cdot dS = \iiint_{V} (\nabla \cdot F) dV$.
Step 3: Analysis
The left side of the equation is a surface integral over a closed surface $S$, and the right side is a volume integral over the region $V$ enclosed by $S$.
Step 4: Conclusion
Therefore, the theorem specifically links surface integrals and volume integrals. Final Answer: (A)
Gauss Divergence Theorem is a fundamental theorem in vector calculus relating the flux through a surface to the divergence within the volume.
Step 2: Meaning
It is mathematically expressed as $\iint_{S} F \cdot dS = \iiint_{V} (\nabla \cdot F) dV$.
Step 3: Analysis
The left side of the equation is a surface integral over a closed surface $S$, and the right side is a volume integral over the region $V$ enclosed by $S$.
Step 4: Conclusion
Therefore, the theorem specifically links surface integrals and volume integrals. Final Answer: (A)
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