Question

A dipole of moment p is placed in uniform electric field E then torque acting on it is given by : -

• A. $\overrightarrow{\tau }=\overrightarrow{P}\cdot \overrightarrow{E}$
• B. $\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}$
• C. $\overrightarrow{\tau }=\overrightarrow{P}+\overrightarrow{E}$
• D. $\overrightarrow{\tau }=\overrightarrow{P}-\overrightarrow{E}$

Answer 1

Answer: (B)

$\overrightarrow{\tau }=\overrightarrow{P}\times \overrightarrow{E}$

Force on charge $+q=F_A=qE$ along direction of vector $\overrightarrow{E}$

Force on charge $-q=F_B=qE$ opposite to direction of $\overrightarrow{E}$

As there two forces are equal, they from a couple

$\begin{array}{c}Torque\left(\tau \right)=Force\times Armofcouple\\ \tau =F\times AB\sin \theta \\ \tau =qE\times AB\sin \theta \\ \tau =qE\times 2a\sin \theta \\ \tau =\left(q\times 2a\right)E\sin \theta \\ \tau =PE\sin \theta ,wherePindipolemovement\\ \tau =P\times E\end{array}$