Q. Electric field on the axis of a small electric dipole at a distance $r$ is ${\overrightarrow{E}}_{1}\ $and$\ {\overrightarrow{E}}_{2}$ at a distance of $2r$ on a line of perpendicular dissector. Then
A) ${\overrightarrow{E}}_{2} = - \frac{{\overrightarrow{E}}_{1}}{8}$
B) ${\overrightarrow{E}}_{2} = - \frac{{\overrightarrow{E}}_{1}}{16}$
C) ${\overrightarrow{E}}_{2} = - \frac{{\overrightarrow{E}}_{1}}{4}$
D) ${\overrightarrow{E}}_{2} = \frac{{\overrightarrow{E}}_{1}}{8}$
Explanation
(b) ${\overrightarrow{E}}_{1} = \frac{1}{4\mu\pi\varepsilon_{0}}.\frac{2\overrightarrow{P}}{r^{3}}$ and
${\overrightarrow{E}}_{2} = - \frac{1}{4\pi\varepsilon_{0}}.\ \frac{\overrightarrow{P}}{{(2r}^{3})} = - \frac{1}{4\pi\varepsilon_{0}}.\frac{\overrightarrow{P}}{{8r}^{3}}$
$\Rightarrow \ \ {\overrightarrow{E}}_{2} = - \frac{{\overrightarrow{E}}_{1}}{16}$
(Here negative sign means direction)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.