Electric Potential Energy of a Cube of 8 protons

AI Thread Summary
The discussion focuses on calculating the electric potential energy of a cube formed by 8 protons, each positioned at the corners of the cube. The potential energy is determined by the work done to assemble the system, with the formula U=q1*q2/(4*pi*epsilon_0*r) being used for pairwise interactions. The user outlines their approach, noting that the total work is the sum of the energies required to bring each proton into the configuration, taking into account various distances between them, including sqrt(2a^2) and sqrt(3)a. The conversation emphasizes the importance of correctly expressing the work done in assembling the system. Ultimately, the total electric potential energy is calculated as the sum of all individual contributions from each pair of protons.
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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