# Potential Energy

1. Apr 10, 2010

### ian2012

A very basic question:

Why is the definition of gravitational potential energy, bringing an object from infinity (or any point of reference) to zero, the negative of the line integral of F.dr ? I am assuming since potential energy in an attractive field , which is defined to be negative, the integral was fixed to lead to this result... or is there a more mathematical reason?

2. Apr 10, 2010

### tiny-tim

Hi ian2012!

potential energy (gravitational electric or whatever) is defined as minus the work done …

and work done = integral of force "dot" displacement …

so PE = -W = -∫ F.dr

(and it has to be minus so that the work-energy theorem works)

3. Apr 11, 2010