Electrostats, Electric potential question. Need a little direction.

In summary, ehild recommends using the equation of potential energy between charges when solving a problem involving two or more charges. If charges q and 8q are placed at a distance r apart, and -q is placed between them, the potential energy of the system will be minimum.
  • #1
PrashntS
25
0

Homework Statement


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

Homework Equations



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

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.
 
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  • #2
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
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 can't post links, because I haven't reached 10 posts yet.
 
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  • #4
Hi PrashntS! Welcome to PF :smile:

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 :wink:
 
  • #5
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
 
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  • #6
ehild said:
There is a real solution, equal to one of the choices. How did you write up the potential energy of the system?

ehild

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. :redface:
 
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  • #7
Answer is, as i have mentioned, D. None of these.
Problem is I can't figure out if my method is even correct.

I am on my summer vocations, so can't get to my instructor for directions.
If some good guy greg here tell me which method he would use i would appreciate it! :-)
 
  • #8
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
ehild said:
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

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
plus or minus infinity? The charges are of opposite sign.ehild
 
  • #11
ehild said:
plus or minus infinity? The charges are of opposite sign.


ehild

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
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
PrashntS said:
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..

Your logic is perfect! :cool:

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


ehild
 
  • #14
ehild said:
Your logic is perfect! :cool:


ehild

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

I'll be posting some other questions as I proceed in the chapter. Would love to ask help again :) :approve:
 
  • #15
PrashntS said:
Really!? :shy: Then I think I am going in correct way!
Thank you ehild for the help. :redface:

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

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

ehild
 

What is electrostatics?

Electrostatics is the study of stationary electric charges and the forces between them.

What is an electric potential?

Electric potential is the amount of work needed to move a unit positive charge from a reference point to a specific point in an electric field, divided by the charge of the test charge.

What is the SI unit for electric potential?

The SI unit for electric potential is volts (V).

What is the difference between electric potential energy and electric potential?

Electric potential energy is the potential energy that an object with a certain charge possesses due to its position in an electric field. Electric potential, on the other hand, is the potential energy per unit charge at a specific point in an electric field.

How can I calculate the electric potential at a point?

The electric potential at a point can be calculated by dividing the electric potential energy by the charge of the test charge at that point.

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