# Electric potential energy

1. Aug 10, 2007

### t_n_p

1. The problem statement, all variables and given/known data

In a model for the hydrogen atom, an electron is in circular orbit at mean distance Ro from the nucleus.

Sketch U as a function of seperation distance r. Write an algebraic expression for the electric potential energy U for a model of this system, i.e. charges +e and -e seperated by distance Ro. Be sure to state the reference you have used for zero potential energy.

The attempt at a solution

The only relevant (?) formula I could find is this one:
V=q/(4pi*εo*r)

How I can sketch the function or write the algebraic expression from that is beyond me though..

2. Aug 10, 2007

### rootX

"charges +e and -e seperated by distance Ro"
so, you know q, and you have the algebraic expresion.
"V=q/(4pi*εo*r)"
And the independent variable is R(or = x).

and put V on the y axis.

3. Aug 10, 2007

### t_n_p

for q do I insert the charge on an electron, 1.60217646 × 10-19.

Edit: figured it out using this method...

http://img524.imageshack.us/img524/4633/potentialyp5.jpg [Broken]

Last edited by a moderator: May 3, 2017
4. Aug 10, 2007

### t_n_p

huh, so i forgot to square radius?

5. Aug 10, 2007

### learningphysics

No no never mind... I totally messed. You did evernthing right tnp, I'm messing up here. sorry lol.

6. Aug 10, 2007

### t_n_p

?
I did?

charges +e and -e, hence q1 = -1.6*10^-19 and q2 = 1.6*10^-19

7. Aug 10, 2007

### learningphysics

Yeah... that's what you did in the diagram... you used q, and Q... I didn't notice that...

8. Aug 10, 2007

### t_n_p

lol, had my confused there for a moment!

9. Aug 10, 2007

### learningphysics

lol. sorry.

one thing though, I don't think a negative r makes sense here since r is the distance... the potential energy between a positive and negative particle is always negative...

10. Aug 10, 2007

### t_n_p

So I wipe the negative x-axis. Thanks for pointing that out!

11. Aug 10, 2007

### t_n_p

Got another Q,

Points A,B,C and D are at corners of a square of sides 2*2μm. Charges of +1nC and -1nC are placed at corners A and B respectively. What is the change in the electric potential from C to D.

A------B
| |
| |
C------D

12. Aug 10, 2007

### learningphysics

Find the potential at D... find the potential at C... subtract the two.

13. Aug 10, 2007

### rootX

I guess you don't need to do any calculations, just analyze the diagram carefully!

14. Aug 10, 2007

### t_n_p

Using this formula?
http://img175.imageshack.us/img175/3082/formulall1.jpg [Broken]

not sure what you're getting at

Last edited by a moderator: May 3, 2017
15. Aug 11, 2007

### learningphysics

If there were two different r's r1 and r2 for q1 and q2, then it would be right...

The potential due to a point charge at a point r away is kq/r or q/4(pi*e0*r)

What is the potential at C due to the charge at A?
What is the potential at C due to the charge at B?

Last edited by a moderator: May 3, 2017
16. Aug 11, 2007

### t_n_p

Does the sign of the charge matter?

For potential at C due to charge at A, I get
(8.99*10^9)(1*10^-9)/(2*10^-6) = 4495000V
Quite a large figure!

For potential at C due to charge at B, I get
(8.99*10^9)(1*10^-9)/(2*root(2)*10^-6) = 3178445V

Total potential at c = 3178445V + 4495000V = 7673444V

17. Aug 11, 2007

### learningphysics

Yes, sign matters... keep the sign of the charge.

18. Aug 11, 2007

### t_n_p

In that case, total potential at C = 1316555V

and

total potential at D = -1316555V

I want the change in the electric potential from C to D, so I subtract C from D?

19. Aug 11, 2007

### learningphysics

Yup that's right.

20. Aug 11, 2007

### t_n_p

cool,
change in electric potential from c to d = -1316555 -1316555 = -2633110V

Final part of the question,
A 3rd charge of +2nC is initially placed at C and then moved to D. What is the change in the potential energy of the system? Take care with sign