Energy of a Collection of Point Charges

When finding the energy of a collection of point charges, all in the same vicinity, we can consider the charges as having been brought from infinity, and find the sum of the energies the charge in the presence of the other changes. This done, add the energies for each charge up.

For example, suppose we have three charges, +3 C, +4 C and +5 C arranged on a straight line, a distance 1 m apart.

Start with a solitary 3C charge.

Bring the 4C charge to 1 m away.

This will require an amount of energy

Now bring the 5C charge to 1 m from the 4C charge.

The 5C charge will acquire energydue to the presence of the 3C charge, anddue to the presence of the $C charge. The total energy acquired by the 5C charge is

The total energy of the collection of charges is

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