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I'm a little confused about something that came up in a lecture a while back. There's nothing about it any books or online seemingly...

The energy for bringing four point charges from infinity to a their relative positions was calculated.

This was done by saying the work to bring in the first is zero, the work to bring in the second is the potential of the first times the charge of the second, the work to bring in the third is the sum of the potentials of the first and second times the charge of the third, and the work to bring in the fourth is the sum of the potentials of the first, second and third. Then the total work U=U1+U2+U3+U4.

Then the next calculation was such that for each charge, there was a sum over the product of the net potential due to the three other charges with that specific charge, and then the total energy of the system W was simply the sum of these products for each of the charges. With a bit of algebra, you could show W=2U.

Now, I'm very confused as to what is actually going on here. I'm a little confused about what the quantites U and W actually represent, and I'm a bit concerned about energy conservation because I feel it implies the work to form the system doesn't equal the potential energy. I realise this may be a bit vague without the actual calculations so if need be I can post some more. If anybody could explain that would be great, thanks.

The energy for bringing four point charges from infinity to a their relative positions was calculated.

This was done by saying the work to bring in the first is zero, the work to bring in the second is the potential of the first times the charge of the second, the work to bring in the third is the sum of the potentials of the first and second times the charge of the third, and the work to bring in the fourth is the sum of the potentials of the first, second and third. Then the total work U=U1+U2+U3+U4.

Then the next calculation was such that for each charge, there was a sum over the product of the net potential due to the three other charges with that specific charge, and then the total energy of the system W was simply the sum of these products for each of the charges. With a bit of algebra, you could show W=2U.

Now, I'm very confused as to what is actually going on here. I'm a little confused about what the quantites U and W actually represent, and I'm a bit concerned about energy conservation because I feel it implies the work to form the system doesn't equal the potential energy. I realise this may be a bit vague without the actual calculations so if need be I can post some more. If anybody could explain that would be great, thanks.

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