Electric Potential Energy Among Multiple Charges

[h4llw4x0r]

Homework Statement

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.

Homework Equations

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

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 =)

 

[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.

 

[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 ?

 

[Shooting Star]

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

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.

 

[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?

 

[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?

 

[Shooting Star]

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

 

[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?

 

[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 shouldn't that be the answer?

what am I doing wrong?

 

[Shooting Star]

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 shouldn't that be the answer?

No.

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?

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

 

[fubag]

thanks a lot shootingstar, helped me a lot, i had misread your post, sorry

 

[fubag]

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

 

[fubag]

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

ok nevermind, i understand the question now

 

[Shooting Star]

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?

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.