An electric dipole is placed in an uniform electric field with the dipole axis making an angle `theta` with the direction of the electric field. The orientation of the dipole for stable equilibrium is

Options

A. `(pi)/(6)`
B. `(pi)/(3)`
C. 0
D. `(pi)/(2)`

Answer

To determine the orientation of an electric dipole for stable equilibrium in a uniform electric field, 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. 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 the Dipole**:
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. **Condition for Stable Equilibrium**:
For stable equilibrium, the potential energy must be at a minimum. Since the potential energy is given by \( U = -pE \cos \theta \), we need to find the angle \( \theta \) that minimizes this expression.

4. **Analyzing the Cosine Function**:
The cosine function \( \cos \theta \) reaches its maximum value of 1 when \( \theta = 0^\circ \). This means that the potential energy \( U \) will be at its minimum value when \( \theta = 0^\circ \).

5. **Conclusion**:
Therefore, the orientation of the dipole for stable equilibrium in a uniform electric field is when the dipole axis is aligned with the direction of the electric field, which corresponds to \( \theta = 0^\circ \).

### Final Answer:
The orientation of the dipole for stable equilibrium is \( \theta = 0^\circ \).