[6.1] Detecting gradient fields
...by looking for their 'swirliness' ("curl"). For each of the following sketches of a vector function of $(x,y)$, use the paddlewheel test to decide if the function could be the gradient of potential function, or not.
$\myv \grad\times\myv F = 0$, everywhere. |
$\myv \grad\times\myv F$ is positive for $x\lt 0$ and negative for $x\gt 0$, and 0 along the $y$ axis. |
$\myv \grad\times\myv F$ is positive (counter-clockwise circulation) everywhere. |
Find one of your vector sketches from yesterday...
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