(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)
S safeer

(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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