An electric dipole placed in a uniform electric field experiences maximum moment of couple when the dipole is placed

Options

A. Against the direction of the field
B. Towards the electric field
C. Perpendicular to the direction of the field
D. At `135^(@)` to the direction of the field

Answer

To solve the problem of determining the orientation of an electric dipole in a uniform electric field that results in the maximum moment of couple (torque), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electric Dipole**:
An electric dipole consists of two equal and opposite charges separated by a distance. The dipole moment (P) is a vector quantity that points from the negative charge to the positive charge.

2. **Torque on an Electric Dipole in an Electric Field**:
When an electric dipole is placed in a uniform electric field (E), it experiences a torque (τ) given by the formula:
\[ \tau = P \cdot E \cdot \sin(\theta) \]
where:
- \( P \) is the dipole moment,
- \( E \) is the electric field strength,
- \( \theta \) is the angle between the dipole moment and the electric field.

3. **Identify Conditions for Maximum Torque**:
To find the maximum torque, we need to maximize the sine function in the torque equation. The sine function reaches its maximum value of 1 when:
\[ \sin(\theta) = 1 \quad \text{at} \quad \theta = 90^\circ \]

4. **Conclusion**:
Therefore, the torque is maximized when the dipole is oriented perpendicular to the direction of the electric field. This means the dipole moment is at a 90-degree angle to the electric field lines.

5. **Final Answer**:
The electric dipole experiences the maximum moment of couple when it is placed **perpendicular to the direction of the electric field**.