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  • Couple experienced by a dipole of moment in a uniform electric field <img alt="\mat

Couple experienced by a dipole of moment \mathrm{\vec{p}} in a uniform electric field \mathrm{\vec{E}} is given by.
\mathrm{\vec{C}=\vec{P} \times \vec{E}}
while its potential energy will be -

Option: 1

\mathrm{\vec{P} \cdot \vec{E}}


Option: 2

\mathrm{2 \vec{P} \cdot \vec{E}}


Option: 3

\mathrm{-\vec{P} \cdot \vec{E}}


Option: 4

\mathrm{-2 \vec{P} \cdot \vec{E}}


Answers (1)

best_answer

The couple acting on the dipole will be -

\mathrm{\begin{aligned} & c=q \cdot 2 l E \sin \theta \\ & c=p E \sin \theta \quad(\because p=q 2 l) \end{aligned}}
Vectirially, 
\mathrm{C=\underset{P}{\rightarrow}\times \underset{E}{\rightarrow}}
Now, as 
\mathrm{\begin{aligned} d U & =C d \theta=P E \sin \theta\ d \theta \\ U & =-P \vec{E} \cos \theta+\text { constant } \end{aligned}}
Assuming the potential energy to be zero at \mathrm{\theta=90^{\circ}}, constant \mathrm{=0}
\mathrm{U=-P \vec{E} \cos \theta=-\vec{P} \vec{E}}

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Anam Khan

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