Question

A dipole of moment $\overrightarrow{p}$ is placed in a uniform electric field $\overrightarrow{E}$. If the force on the dipole is $\overrightarrow{F}$ and the torque is $\overrightarrow{\tau }$. Then :

• A. $\overrightarrow{F}=0$
• B. $\overrightarrow{F}=|\overrightarrow{p}|\overrightarrow{E}$
• C. $|\overrightarrow{\tau }|=\overrightarrow{p}.\overrightarrow{E}$
• D. $\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$

Answer 1

Answer: (A), (D)

$\overrightarrow{F}=0$
$\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$

The force on $+q$ is $\overrightarrow{F_{+}}=q\overrightarrow{E}$ and force on $-q$ is $\overrightarrow{F_{-}}=-q\overrightarrow{E}$
thus net force on dipole is $\overrightarrow{F}=\overrightarrow{F_{+}}+\overrightarrow{F_{-}}=q\overrightarrow{E}-q\overrightarrow{E}=0$
Torque $\tau =\overrightarrow{r}\times \overrightarrow{F}=q\overrightarrow{d}\times \overrightarrow{E}=\overrightarrow{p}\times \overrightarrow{E}$ where $\overrightarrow{p}=q\overrightarrow{d}=$ dipole moment.