Question

Figure 2.34 shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

Answer 1

Four charges of same magnitude are placed at points X, Y, Y, and Z respectively, as shown in the following figure.

A point is located at P, which is r distance away from point Y. 

The system of charges forms an electric quadrupole. 

It can be considered that the system of the electric quadrupole has three charges. 

Charge +q placed at point X 

Charge −2q placed at point Y 

Charge +q placed at point Z 

XY = YZ = a YP = r