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208 CHAPTER 2

Fig. A2.2.2

and therefore,

At this stage, an important approximation is made, namely, that the distance 2d
between the charges in the dipole is negligible compared with r. In other words, the
approximation is made that

It is clear that the validity of the approximation decreases, the closer the ion comes
toward the dipole, i.e., as r decreases.
Making the above approximation, one has [see Eq. (A2.2.4)]

which, by the binomial expansion taken to two terms, gives