Prof.Walter Lewin Says that work done in a binary positive charge system the work done is the work done by the observer to bring the charge from infinity to a desired distance,is the same as the force of interaction moving from that point to infinity.

and because the second integral has known quantities, it relates to [tex]\frac{Qq_o}{4\pi\epsilon_o}\left[ \frac{-1}{r}\right]_r^\infty=\frac{Qq_o}{4\pi\epsilon_or}[/tex]

becase this quantity is charge dependent therefore for attractive bodies the energy will be negative and vice versa.

Now my Queston is:Is work defined as this

taken to be true for all conservative forces and is this the definition (i presume it is) .

Secondly why did he flip the signs of the limits over was it because of the direction of forces.

Thirdly does the thermodynamic concept of work done "on" the system and work done "by" the system apply here too.( i know it does but how?)

If I got the definition right, it's related to there not being any "absolute" potential energy, just differences in potential energy, which relates to the "definition" of potential energy here.