Work required to assemble charged particles

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Homework Help Overview

The problem involves calculating the work required to assemble eight identical charged particles at the corners of a cube. The context is rooted in electrostatics, particularly focusing on the interactions between multiple point charges.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equations related to work and potential energy, with one attempting to apply the formula for potential energy between charges. Others explore the concept of bringing charges from infinity and the calculation of pairs of charges.

Discussion Status

The discussion is ongoing, with participants questioning the number of charge pairs and the interpretation of the cube's geometry. Some guidance has been offered regarding the calculation of pairs, but there is no consensus on the reasoning behind the numbers presented.

Contextual Notes

Participants note the lack of clarity regarding the initial positions of the charges and the assumptions made about their placement. There is also confusion about the geometric aspects of the cube and the calculation of pairs of charges.

SilverGirl
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Homework Statement


How much work is required to assemble eight identical charged particles, each of magnitude q, at the corners of a cube of side s?


Homework Equations


W=deltaU

delta U = kQq/r


The Attempt at a Solution



I've come up with those equations, and was trying to plug the information into delta U. However, all the charges are identical, so there are not two different values for q. But would it be delta U = kq^2/s ??
 
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I take it that the charges come from infinity.

The work required to bring them in from infinity is the sum of the electrostatic energies of the pairs of charges. With 8 charges there are 8*7/2 = 28 such pairs. These can be viewed as the 12 sides of the cube, its 12 surface diagonals and its 4 body diagonals. Be sure to remember that the energy is inversely proportional to the distance, not (like the force) to the distance squared.
 
Almanzo said:
I take it that the charges come from infinity.

The work required to bring them in from infinity is the sum of the electrostatic energies of the pairs of charges. With 8 charges there are 8*7/2 = 28 such pairs. These can be viewed as the 12 sides of the cube, its 12 surface diagonals and its 4 body diagonals. Be sure to remember that the energy is inversely proportional to the distance, not (like the force) to the distance squared.

Yeah it doesn't say where the charges are coming from.

8*7/2 ... where does the 7/2 come from? How are you getting 28 pairs?

12 sides of a cube? Aren't there only 6?
 
Anyone?
 
Does anyone know how they got the 28 pairs?
 

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