When an electric dipole is placed in a uniform electric field, a couple acts on it. The moment of couple will be maximum when the dipole is placed

Options

A. Along the field
B. Perpendicular to the field
C. Against the field
D. At `45^(@)` to the field

Answer

To solve the problem of determining when the moment of the couple on an electric dipole in a uniform electric field is maximum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Dipole and Electric Field**:
- An electric dipole consists of two equal and opposite charges separated by a distance. When placed in an electric field, it experiences a torque due to the forces acting on the charges.

2. **Defining the Torque on the Dipole**:
- The torque (\( \tau \)) experienced by an electric dipole in a uniform electric field (\( E \)) is given by the formula:
\[ \tau = P \cdot E \cdot \sin(\theta) \]
where \( P \) is the dipole moment, \( E \) is the electric field strength, and \( \theta \) is the angle between the dipole moment vector and the electric field vector.

3. **Analyzing the Torque Equation**:
- From the equation, we see that the torque depends on the sine of the angle \( \theta \). The value of \( \sin(\theta) \) varies between -1 and 1.

4. **Finding the Maximum Torque**:
- The torque will be maximum when \( \sin(\theta) \) is at its maximum value. The maximum value of \( \sin(\theta) \) is 1, which occurs at:
\[ \theta = 90^\circ \]
- This means that the dipole should be perpendicular to the electric field for the torque to be maximized.

5. **Conclusion**:
- Therefore, the moment of the couple acting on the dipole will be maximum when the dipole is placed **perpendicular to the electric field**.

### Final Answer:
The dipole should be placed **perpendicular to the electric field** for the moment of the couple to be maximum.

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