Question

$A$ and $B$ are two points on the axis and the perpendicular bisector respectively of a electric dipole. $A$ and $B$ are far away from the dipole and at equal distance from it. The field at $A$ and $B$ are :

• A. ${\overrightarrow{E}}_A={\overrightarrow{E}}_B$
• B. ${\overrightarrow{E}}_A={\overrightarrow{2E}}_B$
• C. ${\overrightarrow{E}}_A=-{\overrightarrow{2E}}_B$
• D. $\left|E_B\right|=\frac{1}{2}\left|E_A\right|,and{\overrightarrow{E}}_{B}isperpendicularto{\overrightarrow{E}}_A$

Answer 1

Answer: (C)

The electric field intensity due to the dipole at the point A on the axis of the dipole is given by
$E_A=\frac{2kp}{r^3}$......(1)
where, $p$ is electric dipole moment, $r$ is the distance of point A from dipole and $k=\frac{1}{4\pi {ϵ}_0}$
The direction of the electric field E is along the axis of the dipole from the negative charge towards the positive charge.
Also, The electric field intensity due to the dipole at the point B on the perpendicular bisector of the dipole is given by
$E_B=\frac{kp}{r^3}$......(2)
The direction of the electric field E is parallel to the axis of the dipole from the positive charge towards the negative charge.
Hence, direction of electric field intensity due to the dipole at the point A is opposite to that of at point B.(refer the figure)
From (1) and (2), we get
$\overrightarrow{E_A}=-2\overrightarrow{E_B}$