   Chapter 16, Problem 40RE

Chapter
Section
Textbook Problem

If the components of F have continuous second partial derivatives and S is the boundary surface of a simple solid region, show that ∬S curl F · dS = 0.

To determine

To show: If the components of F have continuous second partial derivatives ans S is the boundary surface of a simple solid region then ScurlFdS=0 .

Explanation

Formula used:

Write the expression for Divergence Theorem.

EdivFdV=SFdS (1)

If F=Pi+Qj+Rk is a vector field on 3 and P , Q and R have continuous second-order partial derivatives the divcurlF=0 .

Modify equation (1) as follows.

Edivcurl FdV=Scurl FdS

Substitute 0

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