This java applet demonstrates properties of vector fields. You may select one of many vector fields from the Setup menu in the upper right.
The applet shows the potential surface of the vector field, with particles following the field vectors. You may click and drag with the mouse to rotate the view. Also some of the field selections have parameters which may be adjusted.
There is also a 3-D version of this applet (a version with 3-D fields, that is). This version only does 2-D fields, but unlike the 3-D version it can display the potential surface, curl, and divergence, and can also demonstrate Green's theorem and the divergence theorem.
Zip archive of this applet.
Version 1.4a, posted 4/11/14