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

Answer 1

Answer: (B), (C)

The correct options are
B

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

C

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

Electric field due to dipole at the location of Q is:
$E_1=\frac{1}{4\pi {ϵ}_0}\frac{P}{r_3}$ ($\perp$ bisector)

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

From Newton’s third law, force on dipole is equal and opposite.

$E_2$ = Electric field of Q at the location of dipole

$=\frac{1}{4\pi {ϵ}_0}\frac{Q}{r^2}$

$\tau =p{E}_{2}sin{90}^{\circ }=\frac{pQ}{4\pi {ϵ}_0{r}^2}$

$\overrightarrow{\tau }$ is in the direction of $\overrightarrow{p}\times \overrightarrow{E_2}$ or clockwise