Question

The electric field due to an extremely short dipole at distance $r$ from it is proportional to :

• A. $\frac{1}{r}$
• B. $\frac{1}{r^2}$
• C. $\frac{1}{r^3}$
• D. $\frac{1}{r^4}$

Answer 1

Answer: (C)

Let an electric dipole $AB$ is situated in a vacuum. Let $p$ be a point at a distance $r$ from the dipole when $p$ is electric dipole moment, then electric field intensity is given by

$E=\frac{1}{4\pi {\epsilon }_0}\frac{2pr}{{\left(r^2-l^2\right)}^2}$
If $l$ is very small compared to $r(l<<r)$, then $l^2$ may be neglected in comparison to $r^2$. Then
$E=\frac{1}{4\pi {\epsilon }_0}\frac{2p}{r^3}N/C$
$\Rightarrow E\propto \frac{1}{r^3}$