Question

The magnitude of the electric field at a distance $r$ far away along the axis from an electric dipole is $E$. Find the magnitude of the electric field at distance $2r$ along the perpendicular bisector of the dipole.

• A. $E/16$
• B. $E/12$
• C. $E/8$
• D. $E/10$

Answer 1

The correct option is A $E/16$

Let $p$ be the magnitude of dipole moment.

The electric field due to electric dipole at an axial point at a far away distance,

$E=\frac{2kp}{r^3}.........\left(1\right)$

Further, the electric field due to electric dipole at an equatorial point at a far away distance,

$E^{\prime }=\frac{kp}{r^{\prime 3}}$

$\Rightarrow E^{\prime }=\frac{kp}{(2r{)}^3}=\frac{kp}{8r^3}$

from eq.$\left(1\right)$,

$E^{\prime }=\frac{E}{16}$

Hence, option $\left(d\right)$ is the correct answer.