Question

Consider the following statements about electric dipole and select the correct ones.
S1: Electric dipole moment vector $\vec{p}$ is directed from the negative charge to the positive charge.
S2 : 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 $\vec{p}$.
S3 : The electric dipole potential falls off as $\frac{1}{r^2}$ and not as $\frac{1}{r}$
S4 : In a uniform electric field, the electric dipole experiences no net force but a torque $\vec{\tau }=\vec{p}\times \vec{E}$.

• A. S2, S3 and S4
• B. S3 and S4
• C. S2 and S3
• D. all four

Answer 1

Answer: (D)

An electric dipole is a pair of equal and opposite charges $q$ and $-q$ separated by some distance $2a$. Its dipole moment vector $\vec{p}$ has magnitude $2qa$ and is in the direction of the dipole axis from $-q$ to $q$

The electric field due to a dipole at a point $P$ is
$E=\frac{p}{4\pi {\epsilon }_0}\frac{\sqrt{3{\cos }^2\theta +1}}{r^3}(r>>a)$
The electric dipole potential falls off at large distance, as $\frac{1}{r^2}$ not as $\frac{1}{r}$, characteristic of the potential due to a single charge. In a uniform electric field $\vec{E}$, a dipole experiences a torque $\vec{\tau }$ given by $\vec{\tau }=\vec{p}\times \vec{E}$ but experiences no net force.