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Question 22

# 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). 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

PX = r + a

PZ = r - a

Electrostatic potential caused by the system of three charges at point P is given by, Since,   is taken as negligible. It can be inferred that potential, However, it is known that for a dipole, And, for a monopole, ## 1 Comment(s) on this Question

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