An electric dipole placed in a non uniform electric field may experience

Options

A. only a force
B. only a torque
C. both force and torque
D. neither force nor torque

Answer

To solve the question regarding an electric dipole placed in a non-uniform electric field, we will analyze the forces and torques acting on the dipole.

### Step-by-Step Solution:

1. **Understanding the Electric Dipole**:
An electric dipole consists of two equal and opposite charges separated by a distance. It has a dipole moment \( \mathbf{p} \) which is a vector pointing from the negative charge to the positive charge.

2. **Characteristics of a Non-Uniform Electric Field**:
A non-uniform electric field is one where the strength and direction of the electric field vary with position. This means that the electric field \( \mathbf{E} \) is not constant throughout the region.

3. **Torque on the Dipole**:
When an electric dipole is placed in an electric field, it experiences a torque given by the formula:
\[ \tau = \mathbf{p} \times \mathbf{E} \]
This torque tends to align the dipole moment \( \mathbf{p} \) with the electric field \( \mathbf{E} \). The torque is non-zero unless \( \mathbf{p} \) is already aligned with \( \mathbf{E} \).

4. **Force on the Dipole**:
In a non-uniform electric field, the dipole also experiences a net force. The force \( \mathbf{F} \) on the dipole can be expressed as:
\[ \mathbf{F} = \mathbf{p} \cdot \frac{d\mathbf{E}}{dr} \]
Here, \( \frac{d\mathbf{E}}{dr} \) represents the gradient of the electric field. Since the electric field is non-uniform, this gradient is non-zero, leading to a net force acting on the dipole.

5. **Conclusion**:
Therefore, when an electric dipole is placed in a non-uniform electric field, it experiences both a torque and a net force. This means that the correct answer to the question is that the dipole will experience both force and torque.

### Final Answer:
An electric dipole placed in a non-uniform electric field may experience both force and torque.

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