Electric Potential Energy Among Multiple Charges

1. Jan 23, 2008

h4llw4x0r

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

Four point charges, fixed in place, form a square with side length d. (See image)

The particle with charge q is now released and given a quick push; as a result, it acquires speed v. Eventually, this particle ends up at the center of the original square and is momentarily at rest. If the mass of this particle is m, what was its initial speed v?
Express your answer in terms of q, d, m, and appropriate constants. Use k instead of 1/4πe (where e = epsilon). The numeric coefficient should be a decimal with three significant figures.

2. Relevant equations

- Electric Potential Energy equation: U = k((Q1*Q2)/r)
- Relative Kinematics Equations

3. The attempt at a solution

I figured to solve the problem I would need to find the potential energy of the particle with charge q due to each of the other three charged particles and then use the principle of superposition. However, I didn't get the right solution when I worked it out... here's how I was trying to work out the potential energy equation:

U,initial = k(((Q1*Q2)/r1,2)+((Q1*Q3)/r1,3)+((Q1*Q4)/r1,4)+((Q2*Q3)/r2,3)+...)

Can someone help me with my logic here? Thanks =)

Last edited: Jan 23, 2008
2. Jan 23, 2008

Shooting Star

The total PE of q1 due to the other three is reqd. You don't have to do (q2*q3) etc.

Total initial E = total final E. The initial E has got both PE and KE.

3. Feb 9, 2008

babydimples

I got this question too when I was working on my assignment
I was wondering what this part of the question meant

What is the contribution U2q to the electric potential energy of the system, due to interactions involving the charge ?

4. Feb 10, 2008

Shooting Star

The contribution of U2q would be the sum total of the PE due to interaction with the other charges, that is, ∑k(2q)Qi/dist(2q,Qi), where Qi denotes the other three charges.

5. Feb 10, 2008

babydimples

I thought that was to calculate the total potential energy of the system. Now do you do the same for each charge and add it all together?

6. Feb 10, 2008

babydimples

Never mind, i got the total potential energy. I just have one quick question.
What would be the kinetic energy of charge 2q at a very large distance from the other charges?
Would the kinetic energy of the charge 2q be the same as the potential energy of the same charge initally? due to conservation of energy?

7. Feb 10, 2008

Shooting Star

For the total PE of the system, each pair to be considerd once only.

8. Feb 15, 2008

fubag

hi i need help understanding the U_2q has on the total system...i was reading Shooting star's comment and came up with U_2q = (6sqrt(2)*(kq^2))/d but this is not the right answer.

please help. What is the contribution U_2q to the electric potential energy of the system, due to interactions involving the charge 2q?

9. Feb 15, 2008

fubag

i understand in the book that U/q = V, so if we find the electric potential at the center to be equal to (2sqrt(2))(kq)/d)), and then multiply by q shouldnt that be the answer?

what am I doing wrong?

10. Feb 16, 2008

Shooting Star

No.

Refer post #4. Calculate the PE between 2q and the other three charges, and sum the total. Take proper note of the signs.

11. Feb 16, 2008

fubag

12. Feb 16, 2008

fubag

just had a question about the total PE of the system, what does it mean by pairs?

13. Feb 16, 2008

fubag

ok nevermind, i understand the question now

14. Feb 17, 2008

Shooting Star

Somehow, I had missed this question. Sorry.

The KE of the charge 2q very far away, that is infinitely far away, would be equal to the PE at its current position, as you have said, if the other charges are kept fixed.