An electric dipole is placed in a uniform electric field E. We need to find the angle between the positive direction of the dipole moment and the electric field E for which the potential energy of the dipole is minimum.

1. Problem Description

An electric dipole is placed in a uniform electric field E. We need to find the angle between the positive direction of the dipole moment and the electric field E for which the potential energy of the dipole is minimum.

2. Solution Steps

The potential energy $U$ of an electric dipole in a uniform electric field $E$ is given by:

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

where $p$ is the dipole moment, $E$ is the electric field, and $\theta$ is the angle between the dipole moment vector $p$ and the electric field vector $E$.

To minimize the potential energy $U$, we need to minimize $-pE\cos{\theta}$. Since $p$ and $E$ are magnitudes and therefore positive, we need to maximize $\cos{\theta}$. The maximum value of $\cos{\theta}$ is 1, which occurs when $\theta = 0$.

When $\theta = 0$, $U = -pE\cos{0} = -pE(1) = -pE$. This is the minimum potential energy.

When $\theta = \pi/2$, $U = -pE\cos{\pi/2} = -pE(0) = 0$.

When $\theta = \pi$, $U = -pE\cos{\pi} = -pE(-1) = pE$. This is the maximum potential energy.

When $\theta = 3\pi/2$, $U = -pE\cos{3\pi/2} = -pE(0) = 0$.

Therefore, the minimum potential energy occurs when the angle between the dipole moment and the electric field is

0.

3. Final Answer

C. Zero