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# Find the torque due to an external uniform electric field on a dipole of dipole moment $\;\overrightarrow{P}$

$(a)\;\overrightarrow{E} . \overrightarrow{P}\qquad(b)\;\overrightarrow{P} \times \overrightarrow{E}\qquad(c)\;\overrightarrow{E} \times\overrightarrow{P} \qquad(d)\;None\;of\;these$

Can you answer this question?

Answer : (b) $\;\overrightarrow{P} \times\overrightarrow{E}$
Explanation :
The torque of $\;\overrightarrow{F_{1}}\;$ about O
$\overrightarrow{\tau_{1}}=\overrightarrow{OA}\times\overrightarrow{F_{1}}$
$=q\;(\overrightarrow{OA}\times\overrightarrow{E})$
The torque of $\;\overrightarrow{F_{2}}\;$ about O
$\overrightarrow{\tau_{2}}=\overrightarrow{OB}\times\overrightarrow{F_{2}}$
$=-q\;(\overrightarrow{OB}\times\overrightarrow{E})$
$\overrightarrow{\tau_{net}}=\overrightarrow{\tau_{1}}+\overrightarrow{\tau_{2}}$
$=q\;[(\overrightarrow{OA}-\overrightarrow{OB})\times\overrightarrow{E}]$
$=q\;[(\overrightarrow{OA}+\overrightarrow{BO})\times\overrightarrow{E}]$
$=q\;(\overrightarrow{BA}\times\overrightarrow{E})$
$\overrightarrow{\tau_{net}}=\overrightarrow{P}\times\overrightarrow{E}\;.$

answered Feb 11, 2014 by
edited Aug 14, 2014