# (a) Derive an expression for the potential energy of an electric dipole in a uniform electric field. Explain the condition for stable and unstable equilibrium. (b) Is the electrostatic potential necessarily Zero at a point where the electric field is Zero? Give an example to support your answer.

Answers (1)

(a) Deriving an expression of the potential energy of an electric dipole;

$\vec{\varsigma }= \vec{P}\times \vec{E}$
$\vec{\varsigma }= pE\sin \theta$
where, $\vec{\varsigma }= torque$
$p= momentum$
Now
work done $dw= \varsigma \cdot d\theta$
$dw= PE\sin \theta d\theta$
on integrating both side,we have
$w=\int_{\theta 1}^{\theta 2}dw= \int_{\theta 1}^{\theta 2}PE\sin \theta d\theta$
$w= pE\left [ \cos \theta _{1}-\cos \theta _{2} \right ]$
if $\theta _{1}= 0\: and \, \theta _{2}= \theta$
then,$w= pE\left ( 1-\cos \theta \right )$

• when the electric dipole is parallel to electric field the dipole is in the stable equilibrium
• when the electric dipole is antiparallel to the electric field, the dipole is in unstable equilibrium.
(b) The electrostatic potential isn't necessarily Zero at a point where the electric field is Zero.
i.e Such as inside the equipotential surface

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