# Electric Potential Energy defintiion

1. Apr 23, 2012

### the-ever-kid

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

Being in high school my physics teach simply stated that
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
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?)

Last edited: Apr 23, 2012
2. Apr 23, 2012

### Whovian

This is going to be a rubbish post, as it doesn't answer any of your questions, but I suggest you research Gauge Symmetry.

3. Apr 23, 2012

### the-ever-kid

why did you post then ? BTW what is gauge symmetry

4. Apr 23, 2012

### Whovian

Because this should help a bit.

5. Apr 23, 2012

### the-ever-kid

how?

6. Apr 23, 2012

### Whovian

Again, look into Gauge Symmetry.

7. Apr 23, 2012

### factfinder

it is work done in moving unit 'positive' charge, isn't it?

8. Apr 23, 2012

### the-ever-kid

this one is but walter lewin later says that the result is charge sensitive how come as he initially took a charge specific case

9. Apr 23, 2012

### the-ever-kid

read a liitle about gauge smmetry on wikipedia went over my head mindboggling stuff couldnt understand a thing!!!

10. Apr 23, 2012

### the-ever-kid

Doesnt matter as long as the polarity is same

11. Apr 23, 2012

### Whovian

Yea, Wikipedia can be confusing for most math/science topics, probably not the ideal place to start.

12. Apr 23, 2012

### the-ever-kid

how is it related to the topic anyway?

13. Apr 23, 2012

### Whovian

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.

14. Apr 23, 2012

### Khashishi

The sign is arbitrary (a matter of convention) as long as you know what you are doing.