Question

An electric dipole of dipole moment $\overrightarrow{p}$ is placed in a uniform external electric field $\overrightarrow{E}$. Then the

• A. torque experienced by the dipole is $\overrightarrow{E} \times\overrightarrow{p}$
• B. torque is zero if $\overrightarrow{ p}$ is perpendicular to $E\overrightarrow{ E}$
• C. torque is maximum if $\overrightarrow{p }$ is perpendicular to $\overrightarrow{ E}$
• D. potential energy is maximum if $\overrightarrow{ p}$ is parallel to $\overrightarrow{ E}$
• E. potential energy is maximum if $\overrightarrow{p }$ is perpendicular to $\overrightarrow{E }$

Answer 1

Answer: (C)

When an electric dipole of dipole moment $\vec{p}$ is placed in a uniform external electric field $\vec{E}$ , it experiences a torque $\vec{\tau}$ and is given by $\vec{\tau}=\vec{P}\times\vec{E}$
In magnitude,
$\vec{\tau}$ = $PEsin \theta$, where $\theta$ is the angle between $\vec{P}$ and $\vec{E}$
when $\vec{P}$ is perpendicular to $\vec{E}$ i.e. $90^{\circ}$ then
$\tau=PEsin 90^{\circ}=pE$ =maximum, or $\tau_{max}=PE$