Flux across Circle
(see below for directions  read them while the applet loads!)
Directions:

Wait for the applet to load in the gray area above.
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This applet is a limited, easiertouse 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/r^{2} i + y/r^{2} 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
welldefined at the origin, and so the numerical integration of
F.n is not very accurate when the circle passes close to the origin.