a positive amount of work is needed to be done against this force to bring the charges from infinity to a finite distance apart. For unlike charges ( q q < ), the electrostatic force is attractive. In that case, a positive amount of work is needed against this force to take the charges from the given location to infinity. In other words, a negative amount of work is needed for the reverse path (from infinity to the present locations), so the potential energy is negative.
Equation ( . ) is easily generalised for a system of any number of point charges. Let us calculate the potential energy of a system of three charges q , q and q located at r , r , r , respectively. To bring q first from infinity to r , no work is required.
Next we bring q from infinity to r . As before, work done in this step is ( q q q V ( . ) The charges q and q produce a potential, which at any point P is given by , 1P 2P ( . ) Work done next in bringing q from infinity to the point r is q times V , at r , ( q q q q q V ( .
) The total work done in assembling the charges at the given locations is obtained by adding the work done in different steps [Eq. ( . ) and Eq. ( .
)], q q q q q q U ( . ) Again, because of the conservative nature of the electrostatic force (or equivalently, the path independence of work done), the final expression for U , Eq. ( . ), is independent of the manner in which the configuration is assembled.
The potential energy FIGURE . Potential energy of a system of charges q and q is directly