Kinetic energy and speed of system of charges (electric potential)

AI Thread Summary
The discussion revolves around calculating the final velocities of four point charges, each with mass and charge +q, positioned at the corners of a square. The initial electric potential energy of the system is established using the formula U=(kq²/s)(4+√2). To find the final velocities at infinity, the conservation of energy principle is applied, equating initial potential energy to total kinetic energy. Participants suggest considering momentum conservation and the distribution of kinetic energy among the charges, noting the challenge of having four unknowns with limited equations. The importance of symmetry and proper coordinate setup in the two-dimensional system is emphasized for solving the problem effectively.
jpdelavin
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Homework Statement



A square of side s has a point charge at each corner. They all have the same charge +q, but different masses, m1, m2, m3, and m4, respectively. Initially, all of the charges are held at rest until they are released. Of course, they would repel each other and move away from each other until they are very very far. What is their final velocities at infinity (i.e. a long long time after they are released)?

Homework Equations



Ui=kq1q2/r
KE=(1/2)mv2

The Attempt at a Solution



I know that the initial electric potential energy of the system is:

U=(kq2/s)(4+sqrt(2))

To conserve energy, I know that this should also be the total kinetic energy of the system at infinity.

Now, I don't know how to divide the kinetic energy among the charges. If I do this, I can get the final velocity using KE=(1/2)mv2.

Am I correct? Can you give any hints on how to divide the kinetic energy? Should I just divide it equally?
 
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Can you think of any physical principles that might dictate how the energy is distributed? What else might be conserved, for instance?
 
momentum, perhaps? but that still would just leave me with two equations right, and i have four unknowns?
 
Try treating three of the charges as one single charge distribution. The energy of the fourth charge DUE to the distribution of the other three should be constant.
 
jpdelavin said:
momentum, perhaps? but that still would just leave me with two equations right, and i have four unknowns?
You are working in 2 dimensions, don't forget. Also think about symmetries.

It will also help if you set up your coordinates so that the charges are on the axes.
 
@Poley: Is this what you mean?

For particle 4 for example:
.5*m4*v4^2=q*(kq/a+kq/a+kq/(a*sqrt(2))
 
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