Section 2.7 Flux
Another quantity we can measure as we travel around a (closed) curve is called Flux. It measures the degree to which the vector field is aligned with the normal pointing out of the curve.
Learning Objectives:
Geometrically describe a Flux Integral
Define the Flux Integral
Compute a Flux Integral given a parametrization
TYPOS::At 10:24 in the above I put up for a few seconds the computation of flux for the spin field without walking through it as an exercise. Two notes. Firstly, I do yi-xj where in the graphics at the beginning of the video I had -yi+xj. Secondly, there is a missing negative sign in the second integral which is needed to get to my final answer which is (correctly) zero.
Post-Video Activities Post-Video Activities
1.
Consider the field (called a shear field) given by
\(\vec{F}=-y\hat{i}\text{.}\) First try to visualize with pen and paper and you can verify using the
2D vector field plotter we saw previously 1 . Consider the counterclockwise unit circle centered at the origin. Would it have positive, zero, or negative circulation? Now imagine the circle is shifted to it is centred at (0,1). Again, would it have positive, zero, or negative circulation. You can just try to visualize what would happen, and if you wish verify by parametrizing and computing.
2.
Same question as above, but for Flux now
www.geogebra.org/m/QPE4PaDZ
