# Calculating the electric potential engery of the system

1. Sep 28, 2005

### mr_coffee

Hello everyone i'm having problems figuring this out, In the quark model of fundamental particles, a proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 1.32 10-15 m.

(a) Calculate the electric potential energy of the system of only the two "up" quarks.
? eV
(b) Repeat for all three quarks.
? eV

Well i used the following: U_12 = [k*q1*q2]/d = [9.0e9*(2/3)^2*e]/1.32e-15 = 3.0275e24 which is wrong, any ideas what i'm doing wrong?

2. Sep 28, 2005

### Tom Mattson

Staff Emeritus
You forgot to square the "e".

3. Sep 28, 2005

### mr_coffee

Thanks! I don't see how that effects my answer though, because the answer they want is it eV, so how would i get rid of an e, if its now e^2?

4. Sep 28, 2005

### Tom Mattson

Staff Emeritus
But you were calculating in SI units, right? That means that $e=1.602\times10^{-19}C$. If you forget to square it, then your answer will be off by 19 orders of magnitude!

5. Sep 28, 2005

### mr_coffee

ohhhh! i didn't nkow thats what the problem was telling me! infact that makes no sense, how can an electron be positive? I tried it anways, and i got it wrong again, maybe i misunderstood whta you ment. I did the following: U_12 = [k*q1*q2]/d = [9.0e9*((2/3)*1.602e-19)^2]/1.32e-15 = 7.77e-14 eV

6. Sep 28, 2005

### Tom Mattson

Staff Emeritus
The charge on the electron is not positive. It is $-e$.

Examine the units of the left hand side. They are all SI units. That means that your answer will have the SI unit of energy, which is not eV.

7. Sep 28, 2005

### mr_coffee

well he wants the answer in eV, thats what i'm confused on, how would i convert an answer from Joules to eV? id on't even know what eV is. I think he is mnaking it up as he goes along hah

8. Sep 28, 2005

### Tom Mattson

Staff Emeritus
Nevertheless, if you use all SI units in the formula for electric potential energy, your answer will come out with the SI units of energy. That much you should know.

The definition of an electron volt is as follows:

1 electron volt (eV) is defined as the kinetic energy acquired by an electron when it is accelerated through a potential difference of 1 Volt.

That definition is sufficient for you to work out the conversion factor.

Nope, this is all in your book, which you should be reading.

9. Sep 29, 2005

### mr_coffee

Calculate Electric potential engery of the system

Hello everyone, i asked the professor and he told me what to do but i'm still getting the wrong answer for some reason.

In the quark model of fundamental particles, a proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 1.32 10-15 m.
(a) Calculate the electric potential energy of the system of only the two "up" quarks.
eV
(b) Repeat for all three quarks.
eV

So I used the equation:
V = (k)(Q/r + Q/r)
V = (9.0E9)* [(2*1.6E-19)]/1.32e-15m + (2*1.6E-19)]/1.32E-15m)
V = 1454545.455 V
So i need to convert to an eV so i divided by e which is 1.6E-19 as my professor said and other people on the forum and i got:
V = 9.0909E24 eV which is wrong! any ideas? Thanks.

10. Sep 29, 2005

### Staff: Mentor

Is that supposed to be work for (a) or (b)? Either way, consider this: When finding the energy for two quarks there is only one pair, and thus only one use of $V = k Q/r$. But when you add the third quark, how many pairs do you end up with?

11. Sep 29, 2005

### Tom Mattson

Staff Emeritus
mr_coffee:

I've merged your two threads on this question. In the future, please continue with the thread that you started instead of starting a new one for the same question.

12. Sep 29, 2005

### Tom Mattson

Staff Emeritus
Note that this is an electric potential, not a potential energy.

You don't convert from Volts to electron Volts. They have different dimensions. You convert from Joules to electron Volts. eV is a measure of energy.

So, go back to your calculations for potential energy (which had units of Joules) and convert those to eV.

13. Sep 29, 2005

### mr_coffee

Sorry about the repost, i couldn't find my thread!! I just saw Doc's responce, well if V = Kq/R, which is a V or a J/C, I don't see how i'm messing up, is it because i'm adding both pair and doc said i should only use 1, meaning V = KQ/r then i'll still end up with a J/C, why did my professor tell me to divide by e to convert from V to eV?

14. Sep 29, 2005

### Staff: Mentor

As Tom mentioned above, V is the potential, not the potential energy; to get the energy, you have to multiply by the charge, PE = Vq. Given the electric potential due to the first quark at the position of the second ($V = k q_1 /r$), find the potential energy by $k q_1 q_2 /r$. (That's for part (a))

15. Sep 29, 2005

### mr_coffee

ohh i c, so I'm suppose to only use $V = k q_1 /r$ then multiply that by the charge itself, to get PE? Then do i still have to divide by e to conver to eV

16. Sep 29, 2005

### Staff: Mentor

To convert from standard units (J) to eV, you divide by the charge of the electron in Coulombs; in other words 1 eV = 1.60E-19 J. But that conversion should be very easy, since the quark charges are given in terms of electron charge.

17. Sep 29, 2005

### Tom Mattson

Staff Emeritus
If you go to your Profile you can click on "Find all threads started by mr_coffee", and you'll see them (with links) displayed on a page.

18. Sep 29, 2005

### mr_coffee

maybe u have a differnet option because ur a mod, i don't see that option in user cp

19. Sep 30, 2005

### Tom Mattson

Staff Emeritus
My mistake, it's not the User CP. It's your Public Profile page. You can get there by clicking on your own username on any of your posts and selecting, "View Public Profile". You will then be directed to a page that lets you search for your own posts and threads. It's pretty handy.