Question

17. The Green's theorem uses which of the following operation?
O A. Divergence
O B. Gradient
O C. Curl
O D. Laplacian

Answer 1

Answer:

C is the correct answer!

Answer 2

The correct answer is option C) Curl.

• In vector calculus, Green's theorem is the two-dimensional special case of Stokes' theorem. This theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C.

• If we have a line integral, it is converted into a surface integral or the double integral or vice versa using this theorem.

• Let us assume that F is a 2-D vector field, R is some region in the XY-plane and C is the boundary of this region, oriented counterclockwise. Then according to Green's theorem,,

       ∮$_{c}$ F⋅dr = ∬$_{R}$ ( curl F ).k dA

Hence the correct answer is option C) Curl.

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