An electric dipole placed in a nonuniform electric field experience

Options

A. A force but not a torque
B. A torque but not a force
C. A force anda torque
D. Neither a force nor a torque

Answer

To solve the question regarding the behavior of an electric dipole placed in a non-uniform electric field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Dipole**:
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance 'd'. The dipole moment (p) is defined as \( p = q \cdot d \) and it has a direction from the negative charge to the positive charge.

2. **Understanding Non-Uniform Electric Field**:
A non-uniform electric field is characterized by varying strength and direction at different points in space. The electric field lines are closer together in regions of strong electric field and farther apart in regions of weak electric field.

3. **Placing the Dipole in the Electric Field**:
When the dipole is placed in a non-uniform electric field, each charge of the dipole experiences a different electric field strength due to their positions in the field.

4. **Calculating Forces on Each Charge**:
- The force on the positive charge (+q) is given by \( F_1 = +qE_1 \) where \( E_1 \) is the electric field strength at the location of +q.
- The force on the negative charge (-q) is given by \( F_2 = -qE_2 \) where \( E_2 \) is the electric field strength at the location of -q.

5. **Analyzing the Forces**:
Since \( E_1 \) and \( E_2 \) are different (because the electric field is non-uniform), the magnitudes of the forces \( F_1 \) and \( F_2 \) will not be equal. Therefore, the net force \( F_{net} = F_1 + F_2 \) will not equal zero.

6. **Calculating Torque**:
The dipole will also experience a torque due to the forces acting on the two charges. The torque (\( \tau \)) is given by the formula:
\[ \tau = p \times E \]
where \( E \) is the average electric field acting on the dipole. The torque arises because the forces act in opposite directions, creating a rotational effect about the center of the dipole.

7. **Conclusion**:
In a non-uniform electric field, the electric dipole experiences both a net force (due to the difference in forces on the two charges) and a torque (due to the opposing forces creating a rotational effect).

Thus, the correct answer is that an electric dipole placed in a non-uniform electric field experiences **both a force and a torque**.

### Final Answer:
**A force and a torque.**

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