A point dipole $\vec{p} = - p_{0} \hat{x}$ kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance $d$ are, respectively:
(Take V = 0 at infinity)

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$\frac{|\vec{p}|}{4 π ε_{0} d^{2}}, \frac{\vec{p}}{4 π ε_{0} d^{3}}$

$0, \frac{|\vec{p}|}{4 π ε_{0} d^{3}}$

$0, \frac{- \vec{p}}{4 π ε_{0} d^{3}}$

$\frac{|\vec{p}|}{4 π ε_{0} d^{2}}, \frac{- \vec{p}}{4 π ε_{0} d^{3}}$

answer is B.

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Detailed Solution

At equatorial points of a dipole,

potential is zero (V=0).

electric field is given as, $\vec{E} = \frac{- k \vec{p}}{r^{3}}$

so, $\vec{E} = \frac{- \vec{p}}{4 {πε}_{0} d^{3}}$

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