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 determine the position of an electric dipole in a uniform electric field where it experiences the maximum moment of couple (torque), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Torque on a Dipole**:
The torque (\( \tau \)) experienced by an electric dipole in an electric field is given by the formula:
\[ \tau = \mathbf{P} \times \mathbf{E} \]
where \( \mathbf{P} \) is the dipole moment and \( \mathbf{E} \) is the electric field.

2. **Magnitude of Torque**:
The magnitude of the torque can be expressed as:
\[ |\tau| = |\mathbf{P}| |\mathbf{E}| \sin \theta \]
where \( \theta \) is the angle between the dipole moment \( \mathbf{P} \) and the electric field \( \mathbf{E} \).

3. **Maximizing Torque**:
To find the maximum torque, we need to maximize the term \( \sin \theta \). The maximum value of \( \sin \theta \) is 1, which occurs when:
\[ \theta = 90^\circ \]

4. **Conclusion**:
Therefore, the electric dipole experiences maximum torque when it is oriented perpendicular to the direction of the electric field.

### Final Answer:
The electric dipole experiences maximum moment of couple when it is placed perpendicular to the electric field (i.e., at an angle of \( 90^\circ \)).

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