A dipole of electric dipole moment p is placed in a uniform electric field of strength E. If `theta` is the angle between positive direction of p and E, then the potential energy of the electric dipole is largest when `theta` is

Options

A. `(pi)/(4)`
B. `(pi)/(2)`
C. `pi`
D. zero

Answer

To find the angle \( \theta \) at which the potential energy of an electric dipole in a uniform electric field is largest, we can follow these steps:

### Step 1: Understand the Potential Energy Formula
The potential energy \( U \) of an electric dipole moment \( \mathbf{p} \) in a uniform electric field \( \mathbf{E} \) is given by the formula:
\[ U = -\mathbf{p} \cdot \mathbf{E} = -pE \cos \theta \]
where \( \theta \) is the angle between the dipole moment \( \mathbf{p} \) and the electric field \( \mathbf{E} \).

### Step 2: Analyze the Potential Energy
From the formula, we see that the potential energy depends on \( \cos \theta \). The cosine function varies between -1 and 1:
- When \( \cos \theta = 1 \) (i.e., \( \theta = 0^\circ \)), \( U = -pE \) (minimum potential energy).
- When \( \cos \theta = -1 \) (i.e., \( \theta = 180^\circ \)), \( U = pE \) (maximum potential energy).

### Step 3: Determine the Maximum Potential Energy
To maximize the potential energy \( U \), we need to find when \( \cos \theta \) is at its minimum value, which is -1. This occurs at:
\[ \theta = 180^\circ \]
Thus, the potential energy \( U \) is maximized when the dipole is aligned opposite to the direction of the electric field.

### Conclusion
The potential energy of the electric dipole is largest when \( \theta = 180^\circ \).

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