Electric Potential Energy Among Multiple Charges

In summary: Refer to the answer to post #4. KE is determined by the conservation of energy. However, the kinetic energy of the charge 2q would be different at different distances from the other charges.
  • #1
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Homework Statement



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

notSoFast.jpg


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 =)
 
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  • #2
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
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
babydimples said:
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.
 
  • #5
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
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
For the total PE of the system, each pair to be considerd once only.
 
  • #8
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
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?
 
  • #10
fubag said:
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.

fubag said:
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.
 
  • #11
thanks a lot shootingstar, helped me a lot, i had misread your post, sorry
 
  • #12
just had a question about the total PE of the system, what does it mean by pairs?
 
  • #13
fubag said:
just had a question about the total PE of the system, what does it mean by pairs?

ok nevermind, i understand the question now
 
  • #14
babydimples said:
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.
 

1. How is electric potential energy among multiple charges calculated?

The electric potential energy among multiple charges is calculated by multiplying the charge of one of the particles by the sum of the electric potentials caused by all the other particles. This can be represented by the equation U = qΦ, where U is the electric potential energy, q is the charge of the particle, and Φ is the electric potential.

2. What is the unit of measurement for electric potential energy?

The unit of measurement for electric potential energy is joules (J). It can also be measured in electron volts (eV), with 1 eV equal to 1.602 x 10^-19 J.

3. How does the distance between charges affect the electric potential energy?

The electric potential energy is directly proportional to the distance between charges. This means that as the distance between charges increases, the electric potential energy decreases, and vice versa. This can be seen in the inverse square law, where the electric potential energy is inversely proportional to the square of the distance between charges.

4. Can the electric potential energy among multiple charges be negative?

Yes, the electric potential energy among multiple charges can be negative. This occurs when the charges have opposite signs and are attracted to each other. In this case, the electric potential energy is considered to be negative because work must be done to separate the charges and increase their potential energy.

5. How does the number of charges affect the electric potential energy?

The number of charges has a direct impact on the electric potential energy among multiple charges. As the number of charges increases, the electric potential energy also increases. This is because more charges means there is a greater potential for work to be done and for the charges to interact with each other.

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