Skip to main content Contents Prev Up Next \(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
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\)
Section 11.3 Exploring the Divergence
Figure 11.3.1 below shows the relationship between flux and divergence in two dimensions. You can choose the vector field
\(\boldsymbol{\vec{v}}\) by entering its components
\(v_x\) and
\(v_y\text{,}\) move the box by dragging its center, and change the size
\(s\) of the box by moving the slider.
Figure 11.3.1. The relationship between flux and divergence.
Activity 11.3.1 . Exploring Divergence.
Enter the (two-dimensional vector field of your choice into the applet in
Figure 11.3.1 by entering its components. Determine the flux per unit area at several locations by moving the box and adjusting the slider. In each case, compare your result (shown in the applet as
\(\frac{\textrm{flux}}{\textrm{area}}\) ) with the computed value of the divergence at the center of the box (shown as
\(\grad\cdot\vv\big|_P\) ).
What do you notice?
Hint . Start with vector fields whose components are linear functions of \(x\) and \(y\text{,}\) then try more complicated functions.
