Electric Potential Energy of a Cube of 8 protons

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Homework Help Overview

The discussion revolves around calculating the electric potential energy of a cube configuration consisting of 8 protons, each positioned at the vertices of the cube. Participants are exploring the implications of this arrangement on the potential energy calculations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of calculating the total electric potential energy by considering the work done to assemble the protons in the cube configuration. There is mention of specific pairwise potential energy calculations and the distances involved, including the use of square root expressions for distances between certain protons.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and clarifying their understanding of the potential energy calculations. Some have expressed confidence in their approach, while others are verifying the correctness of their expressions and the distances used in their calculations.

Contextual Notes

Participants are working under the assumption that the electric potential energy is defined as the work done to configure the system, and there is a recognition of the complexity introduced by the distances between protons in the cube.

acedeno
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Homework Statement



Suppose we there is a cube (a x a x a) made up of 8 protons. 1 at each point
What is the Electric Potential Energy


Homework Equations


U=q1*q1/4*pi*epsilon_0*r



The Attempt at a Solution


*U12 = Potential Energy to bring 2 to 1*
I'm aware of how to do the question but I'm not sure if I'm expressing it correctly. Remember that the potential energy is the work done configure this system in space.
W1=0
W2=U12
W3=U12+U13
W4=W3+U14
W5=W4+U15
W6=W5+U16
W7=W6+U17
W8=W7+U18

Then the Electric Potential Energy would be = Wtotal = W1+W2 . . . + W8

I am also aware that when I show my equation fully that some of the distances will be sqrt(2a^2)
 
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acedeno said:

Homework Statement



Suppose we there is a cube (a x a x a) made up of 8 protons. 1 at each point
What is the Electric Potential Energy


Homework Equations


U=q1*q1/4*pi*epsilon_0*r



The Attempt at a Solution


*U12 = Potential Energy to bring 2 to 1*
I'm aware of how to do the question but I'm not sure if I'm expressing it correctly. Remember that the potential energy is the work done configure this system in space.
W1=0
W2=U12
W3=U12+U13
The work to bring in the 3rd charge is U13 + U23
W4=W3+U14
And for the 4th charge it's U14 + U24 + U34
W5=W4+U15
W6=W5+U16
W7=W6+U17
W8=W7+U18

Then the Electric Potential Energy would be = Wtotal = W1+W2 . . . + W8
Yes.
I am also aware that when I show my equation fully that some of the distances will be sqrt(2a^2)
 
Thanks a lot! That really helps!
 
Some pairs of protons have a separation distance of (√3)a .
 

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