A point dipole with an electric moment \( p \) oriented in the positive direction of the \( z \)...

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A point dipole with an electric moment \( p \) oriented in the positive direction of the
\( z \) axis is located at the origin of coordinates. Find the projections \( E_{z} \) and \( E_{\perp} \) of the electric field strength vector (on the plane perpendicular to the \( z \) axis at the point \( S \) (see Fig. 3.4)). At which points is \( \mathbf{E} \) perpendicular to \( \mathbf{p} \) ?
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