Final answer:
To approximate the electric potential of a linear quadrupole far away from the charges, a series expansion is used, truncating after the monopole and dipole terms because higher-order contributions become negligible at large distances.
Step-by-step explanation:
The subject in question relates to electric potential far away from a system of charges configured as a linear quadrupole. To approximate this potential at a point far away from the sources, one typically uses a series expansion of the electric potential. The charges in the linear quadrupole consist of 2q at the origin (z=0) and -q each at positions z=a and z=-a on the z-axis. When we're far from the charges, the potential can be approximated by considering only the first few terms in the series, specifically the monopole and dipole moments because the contribution from higher-order moments (quadrupole, octupole, etc.) becomes negligible. The truncation point for the series expansion is justified by the inverse dependence of the series terms on distance; as the observation point gets further away, higher-order terms decrease more rapidly and contribute less to the potential.