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).

Answer

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 - 2*q* 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,

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2019-02-07 23:55:52

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