Question

For the situation shown in the figure (r >> length of dipole) mark out the correct statement(s).

• A. Force acting on the dipole is zero
• B. Force acting on the dipole is approximately $\frac{pQ}{4\pi {\epsilon }_0{r}^3}$
• C. Torque acting on the dipole is $\frac{pQ}{4\pi {\epsilon }_0{r}^2}$ in clockwise direction
• D. Torque acting on the dipole is $\frac{pQ}{4\pi {\epsilon }_0{r}^2}$ in anti-clockwise direction

Answer 1

Answer: (B), (C)

The correct options are
B

Force acting on the dipole is approximately $\frac{pQ}{4\pi {\epsilon }_0{r}^3}$

C

Torque acting on the dipole is $\frac{pQ}{4\pi {\epsilon }_0{r}^2}$ in clockwise direction

Electric field due to dipole at the location of Q is:

$E_1=\frac{1}{4\pi {\epsilon }_0}\frac{P}{r_3}$ (1 bisector)

$\therefore$ Force on $Q=Q{E}_1=\frac{pQ}{4\pi {\epsilon }_0{r}^3}$

From Newton’s third law, force on dipole is equal and opposite.
$E_2$ = Electric field of Q at the location of dipole
$=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}\tau =P{E}_{2}sin{90}^{\circ }=\frac{PQ}{4\pi {\epsilon }_0{r}^2}$
$\overrightarrow{\tau }$ is in the direction of $\overrightarrow{P}\times {\overrightarrow{E}}_2$ or clockwise