Explanation

(b) The electric field on the axis of a dipole of length small compared to point where electric field is to be determined is
$E_{A} = \frac{1}{4\pi\varepsilon_{0}}.\frac{2p}{r^{3}}\ \ \ \ \ \ldots\ldots\ldots\ldots(i)$
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Where p is electric dipole moment.
Intensity at a point on the equatorial line of a dipole is
$E_{E} = \frac{1}{4\pi\varepsilon_{0}}.\frac{p}{r^{3}}NC^{- 1}\ \ \ \ldots.(ii)$
From Eqs. (i) and (ii), we get
$\frac{E_{A}}{E_{E}} = \frac{2p}{r^{3}} \times \frac{r^{3}}{p} = \frac{2}{1}$
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