Question

Consider the following statements about electric dipole and select the correct ones.
$S_1$: Electric dipole moment vector $\vec{p}$ is directed from the negative charge to the positive charge.
$S_2$ : The electric field of a dipole at a point with position vector $\vec{r}$ depends on $|\vec{r}|$ as well as the angle between $\vec{r}$ and $\vec{p}$.
$S_3$ : The electric dipole potential falls off as $\frac{1}{r^2}$ and not as $\frac{1}{r}$.
$S_4$: In a uniform electric field, the electric dipole experiences no net forces but a torque $\vec{\tau }=\vec{p}\times \vec{E}$.

• A. $S_2,S_3$ and $S_4$
• B. $S_3$ and $S_4$
• C. $S_2$ and $S_3$
• D. All four

Answer 1

Answer: (D)

(i) An electric dipole is a pair of equal and opposite charges $q$ and $-q$ separated by same distance $2L$


(ii) The electric field due to a dipole at a point $P$ is
$E=\frac{p}{4\pi {\epsilon }_0}\frac{\sqrt{3{\cos }^2\theta +1}}{r^3}(r\gg a)$
(iii) The electric potential due to dipole in its general position is given by
$V=\frac{k\cdot p\cos \theta }{r^2}$
$V\propto \frac{1}{r^2}$
So, the electric dipole potential falls off as
$\frac{1}{r^2}$ and not as $\frac{1}{r}$.
(iv) In a uniform electric field, the electric dipole experiences no net force but a torque
$\tau =\vec{p}\times \vec{E}$