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  • Couple experienced by a dipole of moment  in a uniform electric field  <img alt="\vec{E}" src

Couple experienced by a dipole of moment \vec{p} in a uniform electric field  \vec{E} is given by.

\vec{c}=\vec{p} \times \vec{E}  while its potential energy will be -
 

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

The couple acting on the dipole will be -


c=q \cdot 2 l E \sin \theta \\


c=p E \sin \theta \quad(\because p=q 2 l)
Vectorially.
c=\vec{p} \times \vec{E}

Now, as

d U=c d \theta=P E \sin \theta d \theta \\
U=-P \vec{E} \cos \theta+\text { constant }

Assuming the potential energy to be zero at \theta=40^{\circ}, constant =0 U=-P \vec{E} \cos c=-\vec{P} \vec{E}

 

Posted by

Sumit Saini

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