Module 2 : Electrostatics
Lecture 9 : Electrostatic Potential
Work done in turning a dipole from equilibrium

If the dipole is twisted by an angle $\theta$ from its stable equilibrium position, work has to be done by the external agency

This work becomes the potential energy of the dipole in this position.

 

Exercise 4

  Energy of a Dipole
 

To calculate energy of a dipole oriented at an angle $\theta$in the electric field, we have to add to the work done above, the energy of the dipole in the equilibrium position. This is equal to the work done in bringing the dipole from infinity to the equilibrium position. The dipole may be aligned in the direction of the field at infinity without any cost of energy. We may now displace the dipole parallel to the field to bring to the equilibrium position. As the negative charge is displaced along the field by an additional distance $a$, the work done is $ -qEa = -pE$, which is the potential energy of the dipole in equilibrium.
The potential energy of the dipole at position $\theta$is

\begin{displaymath}{\cal E} = -pE + pE(1-\cos\theta) = -pE\cos\theta = -\vec p\cdot\vec E\end{displaymath}

The energy is positive if $\theta$is acute and is negative if $\theta$is obtuse.

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