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.
  (If there is no gray area, check your browser settings to make sure that Java is enabled, or try with another browser)

• 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.