Electric intensity due to an electric dipole varies with distance r as $E α r^{n}$ , where ‘n’ is

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Solution

The correct option is D $- 3$
Electric field on axis
$E = \frac{k q}{r_{1}^{2}} - \frac{k q}{r_{2}^{2}} = k q (\frac{r_{2}^{2} - r_{1}^{2}}{r_{1}^{2} r_{2}^{2}}) = k q \frac{(r_{2} - r_{1}) (r_{1} + r_{2})}{r_{1}^{2} r_{2}^{2}}$

$(r_{2} - r_{1}) = d r_{1} = r_{2} = r = \frac{2 k q d}{r^{3}}$

$∴ E α r^{- 3}$
E on radial axis $E_{r}$
$r >> d$
$E_{n e t} = \frac{k g}{(r^{2} + \frac{d^{2}}{4})} \frac{\frac{d}{2}}{\sqrt{r^{2} + \frac{d^{2}}{4}}} = \frac{k q}{(r^{2} + \frac{d^{2}}{4})} \frac{\frac{d}{2}}{\sqrt{r^{2} + \frac{d^{2}}{4}}}$

$E_{r} = \frac{k q d}{r^{3}}$
$∴ E α r^{- 3}$

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