Question

What should be the orientation of an electric dipole in a uniform electric field, that corresponds to stable equilibrium ?

• A. $\theta ={90}^{\circ }$
• B. $\theta ={180}^{\circ }$
• C. $\theta ={30}^{\circ }$
• D. $\theta =0^{\circ }$

Answer 1

The correct option is D $\theta =0^{\circ }$

When the electric dipole aligns itself along the direction of electric field i.e $\overrightarrow{p}||\overrightarrow{E}$, then torque on dipole becomes zero.


Since, we know

$\tau =pE\sin \theta$

$\Rightarrow \tau =0$, when $\theta =0^{\circ }$ or $\theta ={180}^{\circ }$

The net force on electric dipole is always zero in an uniform electric field.

Thus, ${\tau }_{net}=0\&F_{net}=0$ corresponds to equilibrium position for dipole's orientation when $\theta =0^{\circ }$ and $\theta ={180}^{\circ }$.

Now electrostatic potential energy of dipole,

$U=-\overrightarrow{p}.\overrightarrow{E}=-pE\cos \theta$

$\Rightarrow U=-pE\cos 0^{\circ }=-pE$

$\Rightarrow U=-pE$ (when $\theta =0^{\circ }$)

Similarly, $U=-pE\cos {180}^{\circ }=-(-pE)$

$\Rightarrow U=+pE$ (when $\theta ={180}^{\circ }$)

Therefore, for $\theta =0^{\circ }$, the potential energy is minimum.

$U_{min}=-pE$

$\therefore \theta =0^{\circ }$ corresponds to stable equilibrium position of dipole.

$\begin{array}{c}\text{Why this question}?\\ \text{Tip: The equilibrium position corresponding to}\\ \theta ={180}^{\circ }\text{is unstable equilibrium because Potential}\\ \text{energy of dipole is maximum}\end{array}$