# Electrostats, Electric potential question. Need a little direction.

1. Jun 9, 2012

### PrashntS

1. The problem statement, all variables and given/known data
Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge -q be placed between them so that the electrical potential energy of the system is minimum.
a). at a distance r/3 from 2q
b). at a distance 2r/3 from 2q
c). at a distance r/16 from 2q
d). none of these

2. Relevant equations

PE of system= PE between all the individual charges.
EPE of two point charges can be given as: 1/4πε * q1*q2 / r

3. The attempt at a solution

I simply derived the equation of potential energy of system, which is:
http://i46.tinypic.com/nvt72s.jpg
Then I differentiated the equation to find out the value of x where potential energy is minimum.
I got x = 2r + 8 +- sqrt( 5r^2-8r+16)

Now the problem is I dnt know whether my solution is correct. Since the question is MCQ, i ticked none of these. which, hopefully was correct. Need help.

Last edited by a moderator: Jun 9, 2012
2. Jun 9, 2012

### vela

Staff Emeritus
Back up a bit and tell us your initial expression for the potential energy before you did any algebra. Your expression doesn't look right to me.

3. Jun 9, 2012

### PrashntS

Here is my full working for the initial part. Got same expression each time I did the question.

http:// i46.tinypic . com/33w9s92.jpg

PS: I cant post links, because I havent reached 10 posts yet.

Last edited: Jun 10, 2012
4. Jun 10, 2012

### Infinitum

Hi PrashntS! Welcome to PF

I didn't get a real solution either, so your answer seems correct. But the method you've used is a pretty long one. I'd recommend taking out the constant term 8/r and 2kq2 before differentiating so that it is waay easier

5. Jun 10, 2012

### ehild

There is a real solution, equal to one of the choices. Although that minimum potential energy meant minimum absolute value, so maximum energy... How did you write up the potential energy of the system????

ehild

Last edited: Jun 10, 2012
6. Jun 10, 2012

### Infinitum

Hmm, I probably made a mistake then.....I'll recheck it.

Edit: After a brief look-back, it does have a solution indeed as ehild says. I missed a negative sign leading to no solutions...Apologies.

Last edited: Jun 10, 2012
7. Jun 10, 2012

### PrashntS

Answer is, as i have mentioned, D. None of these.
Problem is I cant figure out if my method is even correct.

I am on my summer vocations, so cant get to my instructor for directions.
If some good guy greg here tell me which method he would use i would appreciate it! :-)

8. Jun 10, 2012

### ehild

If the answer is D then they really meant minimum energy. What is the potential energy between a positive and a negative charge if they are at zero distance from each other?

ehild

9. Jun 10, 2012

### PrashntS

As far as I know, it should be ∞ as r->0 PF->∞
Let me know if i am wrong, I have started the chapter a day ago.

10. Jun 10, 2012

### ehild

plus or minus infinity? The charges are of opposite sign.

ehild

11. Jun 10, 2012

### PrashntS

I guess minus infinity.. Since PE is scaler, we need to put sign in the expression.. And this would lead to negative side of infinity as far as mathematics is concerned..

12. Jun 10, 2012

### PrashntS

I have this thing in my mind:
PE of system is PE due to interaction between individual charges.
Now, if -q coincides with either 2q or 8q, the resultant PE would be -∞.
Any finite value (in this case interaction between 2q and 8q) when added to -∞ will be equal to -∞.

And since the problem is expecting the place where the PE is minimum, we are getting -∞, which is surely minimum. So the answer should be D.

Now, I don't really know if my logic is correct or not, because I am trying to reach answer somehow..

13. Jun 10, 2012

### ehild

(Although we do not call ±infinity maximum/ minimum in Maths.)

ehild

14. Jun 10, 2012

### PrashntS

Really!? :shy: Then I think I am going in correct way!
Thank you ehild for the help.

I'll be posting some other questions as I proceed in the chapter. Would love to ask help again :)

15. Jun 10, 2012

### ehild

I would love to see more of your problems...

ehild