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. `3pi//2`

Answer

To solve the problem of determining the angle at which an electric dipole has minimum potential energy when placed in a uniform electric field, we can follow these steps:

### Step-by-Step Solution:

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

2. **Finding the Condition for Minimum Potential Energy**:
To find the angle that minimizes the potential energy, we need to analyze the expression \( U = -pE \cos \theta \). The potential energy is minimized when \( \cos \theta \) is maximized because of the negative sign in front of the equation.

3. **Maximizing \( \cos \theta \)**:
The maximum value of \( \cos \theta \) is 1, which occurs when:
\[ \theta = 0^\circ \]
This means that the dipole moment is aligned in the same direction as the electric field.

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

### Final Answer:
The angle at which the electric dipole has minimum potential energy when placed in a uniform electric field is \( 0^\circ \).

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