Question

Which of the following assertions accurately describes Gauss's theorem?

• A. It connects a line integral of a vector field with a surface integral of the field's curl.
• B. It links a surface integral of a vector field with a line integral of the field's curl.
• C. It correlates a line integral of a vector field with a volume integral of the field's curl.
• D. It associates a surface integral of a vector field with a volume integral of the field's divergence.

Hint:

Gauss's theorem is useful for converting surface integrals into volume integrals and vice versa, especially when dealing with electric fields and fluid flow.

Answer 1

The Correct Option is D

Gauss's theorem, also known as the Divergence theorem, relates the surface integral of a vector field through a closed surface to the volume integral of the divergence of the field over the region inside the surface. This is a fundamental theorem in vector calculus.