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The electric field intensity $\overrightarrow{\mathrm{E}}$, due to an electric dipole of moment $\vec{p}$, at a point on the equatorial line is
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parallel to the axis of the dipole and opposite to the direction of the dipole moment $\overrightarrow{\mathrm{p}}$
The resultant intensity at a point on equatorial line is $\overrightarrow{\mathrm{E}} . \overrightarrow{\mathrm{E}}$ is parallel and opposite to direction of $\overrightarrow{\mathrm{p}}$.
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