An electric dipole when placed in uniform electric field has zero potential energy. The angle between dipole moment and electric field is ....

Options

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

Answer

To solve the problem of finding the angle between the dipole moment and the electric field when the potential energy is zero, we can follow these steps:

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

### Step 2: Set the potential energy to zero
According to the problem, the potential energy is zero:
\[ U = 0 \]

### Step 3: Substitute the potential energy equation
Substituting the expression for potential energy into the equation gives:
\[ -PE \cos \theta = 0 \]

### Step 4: Analyze the equation
For the product \( -PE \cos \theta \) to be zero, either \( P \) or \( E \) must be zero, or \( \cos \theta \) must be zero. Since both \( P \) and \( E \) are non-zero (as they are defined dipole and electric field), we focus on:
\[ \cos \theta = 0 \]

### Step 5: Solve for the angle
The cosine of an angle is zero at:
\[ \theta = 90^\circ \]
or in radians:
\[ \theta = \frac{\pi}{2} \]

### Conclusion
Thus, the angle between the dipole moment and the electric field when the potential energy is zero is:
\[ \theta = 90^\circ \]

### Final Answer
The angle between the dipole moment and the electric field is **90 degrees**.

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