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The energy required to assemble a system of point charges is

  • A.the product of the total charge and the mean potential over space
  • B.zero
  • C.the sum of the work done in bringing each charge from infinity in turn
  • D.the sum of the potentials at the positions of all the charges

Answer: C

The first charge costs nothing, the second is brought in against the field of the first, and so on, which is why the total is a sum over pairs. Written compactly it is half the sum of each charge times the potential of the others at its position.

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