Therefore,                                                          .......................(2.88)

Electrostatic Energy and Energy Density

We have stated that the electric potential at a point in an electric field is the amount of work required to bring a unit positive charge from infinity (reference of zero potential) to that point. To determine the energy that is present in an assembly of charges, let us first determine the amount of work required to assemble them. Let us consider a number of discrete charges Q₁, Q₂,......., Q_N are brought from infinity to their present position one by one. Since initially there is no field present, the amount of work done in bring Q₁ is zero. Q₂ is brought in the presence of the field of Q₁, the work done W₁= Q₂V₂₁ where V₂₁ is the potential at the location of Q₂ due to Q₁. Proceeding in this manner, we can write, the total work done

.................................................(2.89)

Had the charges been brought in the reverse order,

.................(2.90)