Calculate Speed of a Charged Particle in a Square

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Homework Help Overview

The problem involves calculating the speed of a charged particle that is initially given a velocity while other charges are held stationary. The context is set within a square configuration of charges, and the goal is to express the final speed of the moving charge as it moves infinitely far from the others, using principles of energy conservation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss applying conservation of energy principles, questioning the initial potential energy of the moving charge, and the contributions of other charges to the potential energy. There are attempts to set up equations based on energy conservation, but some participants express uncertainty about the correctness of their formulations.

Discussion Status

The discussion is ongoing, with participants providing guidance on using conservation of energy and clarifying the role of potential energy at infinity. There is a mix of interpretations regarding the initial conditions and potential energy contributions from multiple charges, indicating a productive exploration of the problem.

Contextual Notes

Participants are working under the assumption that potential energy is zero at infinity, and there is a focus on correctly identifying the initial potential energy contributions from the other charges in the system.

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Homework Statement



IP One of the - charges in the figure (sqaure, with one charge at each corner) is given an outward "kick" that sends it off with an initial speed while the other three charges are held at rest. If the moving charge has a mass , what is its speed when it is infinitely far from the other charges?
Express your answer in terms of the variables (Q (charge), m, v and a (a is the length of the side of one sqaure)) and appropriate constants.

Im not sure how to start. Can anyone help?
 
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First draw a picture and show us. Then try to apply conservation of energy as the Coulomb force is conservative.

ehild
 
also use the fact that potential energy is 0 at infinity. tell us what you get.
 
I am working on the same problem and have attached a link for the diagram:
http://session.masteringphysics.com/problemAsset/1126168/2/Walker4e.ch20.Pr100.jpg

I took the advice already given on this board and used conservation of energy and started with:
1/2mvo^2+K-Q+Q/a=1/2mvf^2+0
(0 because as stated above PE at infinity is 0) so we are left with:

1/2mvo^2+K-Q+Q/a=1/2mvf^2

Im not quite sure where to go from here though.
 
I do not get your equation. It is certainly wrong. What is the initial potential energy of the selected charge?

ehild
 
Would it not be the equation kq/r?

I used K(-Q)(+Q)/a (because the the charges are Q with positive or negative and the length between them is a..hope that makes a bit more sense.
 
It is better now. But that selected charge has got potential energy from all the other three charges.

ehild
 

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