Flux across Circle
(see below for directions - read them while the applet loads!)
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This applet is a limited, easier-to-use version of the more general applet
on Curves and vector fields, tailored
specifically for PS 8 Problem 4.
The goal is to visualize the flux of the vector field
F=x/r2 i + y/r2 j
across a circle of radius a centered at (1,0).
Use the bottom slider to control the radius a. Observe what happens
when a changes between values lower than 1 and values greater than 1.
The applet displays (just under the two sliders) the value of F.n
at a chosen point on the circle (controlled by the top slider), as well as
the flux of F across the portion of circle corresponding to angles
from 0 to the chosen value. (leave the top slider in the rightmost position
if you want the total flux across the entire circle)
For values of a close to 1, the applet will give a different answer
from the one you have computed. This is because the vector field is not
well-defined at the origin, and so the numerical integration of
F.n is not very accurate when the circle passes close to the origin.