This applet allows you to visualize vector fields and their divergence and curl, as well as work done by a field.
Choose a field from the drop-down box. Drag the curl paddle and divergence dot around the field to see how these change.
Select a path to see the work done by the field along the path.
Slightly modified version of the worksheet by George Sturr (http://tube.geogebra.org/user/profile/id/13883).

Find a vector field from among the choices given for which the work done along any closed path you make is zero. Can you find a scalar function f such that the gradient of f is equal to the vector field?