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Contents Index Calc Dark Mode Prev Up Next \(\newcommand{\R}{\mathbb{R}}
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Activity 13.7.2 . Matching Visual Measurements to Algebraic Calculations.
Remember that the circulation density of a vector field \(\vF=\langle F_1,F_2\rangle\) at a point \((a,b)\) is calculated as
\begin{equation*}
\text{Circulation Density at the point }(a,b)= \frac{\partial F_2}{\partial x} (a,b)-\frac{\partial F_1}{\partial y} (a,b)\text{.}
\end{equation*}
The circulation density will be positive when a small spinner placed at \((a,b)\) will spin counterclockwise, negative when the spinner will move clockwise, and zero when the spinner does not rotate.
For each of the vector fields given below, answer the following questions:
What is the formula for the circulation density of the vector field?
For what points will you have a positive circulation density?
For what points will you have a negative circulation density?
For what points will you have a zero circulation density?
(a)
(b)
(c)
\(\langle 1-x,xy\rangle\)
