A Visual Curl Applet

This applet is designed to build intuition about the curl of a vector field.
• The applet has a control window, a Vector Field window, and a Scaled Perp flow window.
• The control panel lets you define the vector field V=(p,q).  It gives readouts for the value of P0 along with V, and its curl, all evaluated at P0.
• The Vector Field window shows the the vector field V with a viewing window centered around a point P0 whose coordinates are controlled by the boxes and buttons of the control panel.  The curl at P0 is shown by a vertical blue bar.  A green circle of radius loopscale is centered at the point.  The loopvectors checkbox plots V at points on this loop.  Red arrows from the loop give the tangential component of V.
• The control panel lets you set the viewing window along with the density and scaling factor of the vector field.  You can also scale the size of the green circle and the length of the red vectors.
• The Scaled window sets up for the integral definition of curl.  (Recall that the divergence of V at P0 is the limit as R goes to zero of the integral of the normal component of the flow appropriatelty scaled for the lenght of the circle.)  The NormalFlowAntipodal window looks at the sum of the perpendicular component of the field at antipodal points.  We would routinely expect the flow much of the flow from antipodal points to cancel out, so that is eliminated.

Things to notice:
• The field (-y,x) has a steady curl of 2.
• The field (-y^2, x) has constant curl on vertical lines
• The field (x,y) has a steady curl of 0.  Away from the origin, the flow in at one point is canceled by the flow out at the antipodal point.
• The field (2,3) has steady curl of 0.
• The curl is positive if the field is rotating counter clockwise

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University.  It is used with permission.   Go to the Banchoff Applet Help page.