#
Path Integral

## Description

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.**
**

## Question

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