Question

$A$ 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

• A. $\vec{E}_{A}=\vec{E}_{B}$
• B. $\vec{E}_{A}=2 \vec{E}_{B}$
• C. $\vec{E}_{A}=-2 \vec{E}_{B}$
• D. $\left|\vec{E}_{B}\right|=\frac{1}{2}\left|\vec{E}_{A}\right|$, and $\vec{E}_{A}$ is perpendicular to $\vec{E}_{B}$

Answer 1

Answer: (C)

Electric field due to dipole at axial position is
$E_{\text {axial }}=\frac{1}{4 \pi \varepsilon_{0}} \frac{2 p}{r^{3}}$ (along the dipole moment)
Electric field due to dipole at equatorial position
$E_{\text {eq }}=\frac{1}{4 \pi \varepsilon_{0}} \frac{p}{r^{3}}$ (opposite to dipole moment)
Hence $\vec{E}_{A}=-2 \vec{E}_{B}$