Question

If this dipole were kept in a uniform external electric field $E_0$, diagrammatically represent the position of the dipole in stable and unstable equilibrium and write the expressions for the torque acting on the dipole in both the cases.

Answer 1

Let the dipole is kept in two positions (a) and (b) in constant electric field $E_o$ as shown in the figure.

Case (a) : Angle between dipole and the electric field $\theta =0^o$

Potential energy of dipole $U=-P{E}_o\cos \theta$

$\therefore$ $U=-P{E}_o\cos 0^o=-P{E}_o$

Thus the dipole is said to be in stable equilibrium.

Torque $\tau =P{E}_o\sin \theta$

$\therefore$ $\tau =P{E}_o\sin 0^o=0$

Case (b) : Angle between dipole and the electric field $\theta ={180}^o$

Potential energy of dipole $U=-P{E}_o\cos {180}^o=P{E}_o$

Thus the dipole is said to be in unstable equilibrium.

Torque $\tau =P{E}_o\sin {180}^o=0$