# Electric Potential Energy of a Cube of 8 protons

## 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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Redbelly98
Staff Emeritus
Homework Helper

## 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!

SammyS
Staff Emeritus