\( A \) and \( B \) are two points on the axis and the perpendicular bisector, respectively, of ...

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\( A \) and \( B \) are two points on the axis and the perpendicular bisector, respectively, of an electric dipole. \( A \) and \( B \) are far away from the dipole and at equal distances from it. The fields at \( A \) and \( B \) are \( \vec{E}_{A} \) and \( \vec{E}_{B} \). Then
(1) \( \vec{E}_{A}=\vec{E}_{B} \)
(2) \( \vec{E}_{A}=2 \vec{E}_{B} \)
(3) \( \vec{E}_{A}=-2 \vec{E}_{B} \)
(4) \( \left|\vec{E}_{B}\right|=\frac{1}{2}\left|\vec{E}_{A}\right| \), and \( \vec{E}_{A} \) is perpendicular to \( \vec{E}_{B} \).
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