Question 705036

SCQHARD

A point electric dipole $\vec{P} = p_x\hat{i}$ is placed at a vertical distance $d$ above a grounded infinite conducting $xy$ plane. At a point $\vec{r}$ ( $r \gg d, z > 0$ ) far away from the dipole, the electrostatic potential $V(r)$ varies approximately as

(A)

$\frac{1}{r^2}$

(B)

$\frac{1}{r^6}$

(C)

$\frac{1}{r^3}$

(D)

$\frac{1}{r^4}$

Detailed Solution

The system consists of the original dipole and its image dipole created by the conducting plane. These two dipoles effectively form a quadrupole. The potential of a dipole falls as $1/r^2$ , while the potential of a quadrupole falls as $1/r^3$ .

So, $1/r^3$ is the correct answer.

Free Exam

Boost Your Exam Preparation!

Move beyond just reading solutions. Access our comprehensive Test Series, original Mock Tests, and interactive learning modules. Many premium tests are completely free!

Original Mocks & Regular Test Series
Real NTA-like Interface with Analytics
Many Free Tests Available