   Chapter 16, Problem 9RCC

Chapter
Section
Textbook Problem

Suppose F is a vector field on ℝ3.(a) Define curl F.(b) Define div F.(c) If F is a velocity field in fluid flow, what are the physical interpretations of curl F and div F?

(a)

To determine

To define: The curl of vector field F on 3 .

Explanation

Consider a vector field F on 3 as F(x,y,z)=Pi+Qj+Rk and the partial derivatives of components of F exist.

Write the expression for del operator () ,

=ix+jy+kz

The curl of F(x,y,z)=Pi+Qj+Rk is defined as follows,

curlF=×F

Substitute ix+jy+kz for and Pi+Qj+Rk for F

(b)

To determine

To define: The divF of vector field F on 3 .

(c)

To determine

To express: The physical interpretations of curlF and divF for velocity field in fluid flow.

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