An electric dipole when placed in a uniform electric field `E` will have minimum potential energy, if the positive direction of dipole moment makes the following angle with `E`

Options

A. `pi`
B. `pi//2`
C. Zero
D. `3 pi//2`

Explanation

To determine the angle at which an electric dipole has minimum potential energy when placed in a uniform electric field \( E \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Dipole**: An electric dipole consists of two equal and opposite charges separated by a distance \( d \). The dipole moment \( \vec{p} \) is defined as:
\[ \vec{p} = q \cdot \vec{d} \]
where \( q \) is the magnitude of one of the charges and \( \vec{d} \) is the vector pointing from the negative charge to the positive charge.

2. **Potential Energy of a Dipole in an Electric Field**: The potential energy \( U \) of an electric dipole in a uniform electric field \( \vec{E} \) is given by the formula:
\[ U = -\vec{p} \cdot \vec{E} = -pE \cos \theta \]
where \( \theta \) is the angle between the dipole moment \( \vec{p} \) and the electric field \( \vec{E} \).

3. **Analyzing the Potential Energy**: The potential energy \( U \) will be minimum when the cosine term is maximized. Since \( \cos \theta \) reaches its maximum value of 1 when \( \theta = 0^\circ \), this corresponds to the dipole moment being aligned with the electric field.

4. **Finding Minimum Potential Energy**: To find the angle for minimum potential energy, we need to consider the behavior of the potential energy function:
- If \( \theta = 0^\circ \) (dipole aligned with the field), \( U = -pE \).
- If \( \theta = 180^\circ \) (dipole anti-aligned with the field), \( U = pE \), which is maximum.

5. **Conclusion**: Therefore, the angle \( \theta \) at which the electric dipole has minimum potential energy in a uniform electric field is:
\[ \theta = 0^\circ \]

### Summary:
The electric dipole will have minimum potential energy when the angle between the dipole moment and the electric field is \( 0^\circ \), meaning the dipole is aligned with the electric field.