Question

If a dipole of dipole moment $\overrightarrow{p}$ is placed in a uniform electric field $\overrightarrow{E}$, then torque acting on it is given by :

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

Answer 1

The correct option is B $\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$

Dipole moment of the dipole p and uniform Electric field $E$. we know that dipole moment $p=qa$ (where q is charge and a is the dipole length).And when a dipole of Dipole moment p is placed in a uniform Electric field E , the torque $\tau =Eitherforce\times \text{perpendicular distance between the two forces}=qaEsin\theta$ or $\tau =pEsin\theta$ or $\tau =p\times E$