## Electric Potential Energy

I've Had this doubt from a long time back :

Being in high school my physics teach simply stated that
 "potential energy in an attractive system is negative"
No explanations given.

To quench my thirst I went through books and things . I found one difinitive result :

a:

In this Video http://bit.ly/wl8-0204
• 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.
• $$\mathcal{W}_{\infty\rightarrow r}=\int_\infty^r\vec{F}_{obs}\cdot d\vec{r}=\int^\infty_r\vec{F}_{elec}\cdot d\vec{r}$$
• and because the second integral has known quantities, it relates to $$\frac{Qq_o}{4\pi\epsilon_o}\left[ \frac{-1}{r}\right]_r^\infty=\frac{Qq_o}{4\pi\epsilon_or}$$
• 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
 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
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?)
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 This is going to be a rubbish post, as it doesn't answer any of your questions, but I suggest you research Gauge Symmetry.
 why did you post then ? BTW what is gauge symmetry

## Electric Potential Energy

Because this should help a bit.
 how?
 Again, look into Gauge Symmetry.
 it is work done in moving unit 'positive' charge, isn't it?
 this one is but walter lewin later says that the result is charge sensitive how come as he initially took a charge specific case
 read a liitle about gauge smmetry on wikipedia went over my head mindboggling stuff couldnt understand a thing!!!

 Quote by factfinder it is work done in moving unit 'positive' charge, isn't it?
Doesnt matter as long as the polarity is same

 Quote by the-ever-kid read a liitle about gauge smmetry on wikipedia went over my head mindboggling stuff couldnt understand a thing!!!
Yea, Wikipedia can be confusing for most math/science topics, probably not the ideal place to start.
 how is it related to the topic anyway?
 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.
 The sign is arbitrary (a matter of convention) as long as you know what you are doing.

 Tags electricity, electrostatics, potential energy