Explain the positions (orientations) of a dipole in stable equilibrium,unstable equilibrium,and when the potential energy is zero.

(N/A) The potential energy $U$ of a dipole placed in a uniform electric field $\vec{E}$ is given by $U = -\vec{p} \cdot \vec{E} = -pE \cos \theta$,where $\theta$ is the angle between the dipole moment $\vec{p}$ and the electric field $\vec{E}$.
$(i)$ Stable Equilibrium: When $\vec{p}$ is parallel to $\vec{E}$,$\theta = 0^{\circ}$.
$U = -pE \cos(0^{\circ}) = -pE$. This is the minimum potential energy state,representing stable equilibrium.
(ii) Unstable Equilibrium: When $\vec{p}$ is anti-parallel to $\vec{E}$,$\theta = 180^{\circ}$.
$U = -pE \cos(180^{\circ}) = pE$. This is the maximum potential energy state,representing unstable equilibrium.
(iii) Zero Potential Energy: When $\vec{p}$ is perpendicular to $\vec{E}$,$\theta = 90^{\circ}$.
$U = -pE \cos(90^{\circ}) = 0$. This represents the state where the potential energy of the dipole is zero.