Path Integral



A cursor is shown in an x-y graph. The cursor can be dragged around the graph and its path is marked as it is moved.  The data are sent to a DataTable which shows x, y, and the value of the path integral, F.dl.  Data are shown for a cursor starting at x=5 and y=0.


What is the value of F? Is it conservative?  


Instructor Resources

Answer: dl /dl (or just dl hat). It is not conservative. To determine this, students must consider the best path to examine. The path shown above is actually not very helpful. A more useful path is one with a component in only one direction at a time. For a path solely in the x direction, one finds the value of the integral to be the distance traveled in the x direction. The same thing occurs in the y direction. Since this path integral depends only on the distance, not the displacement, this is not a conservative F. Hence, the integral F.dl is not equal to 0, as shown by the table above.
Script Author: Mario Belloni