An electric dipole is kept inside a uniform electric field. If Fis the magnitude of net force on dipole and `tau` is magnitude of net torque, then

Options

A. F must be zero, `tau` must be zero
B. F must not be zero, `tau` must not be zero
C. F Must not be zero, `tau` must be zero
D. F must be zero, `tau` may be non-zero

Explanation

To solve the problem regarding the electric dipole placed in a uniform electric field, we will analyze the forces and torques acting on the dipole step by step.

### 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 \( \mathbf{p} \) is defined as:
\[ \mathbf{p} = q \cdot d \]
where \( \mathbf{p} \) is a vector pointing from the negative charge to the positive charge.

**Hint**: Remember that the dipole moment is a vector quantity and depends on the magnitude of the charges and the distance between them.

2. **Analyzing the Forces**:
When the dipole is placed in a uniform electric field \( \mathbf{E} \), the positive charge experiences a force \( \mathbf{F}_+ = q \mathbf{E} \) in the direction of the field, and the negative charge experiences a force \( \mathbf{F}_- = -q \mathbf{E} \) in the opposite direction.

**Hint**: The forces on the two charges are equal in magnitude but opposite in direction.

3. **Calculating the Net Force**:
The net force \( \mathbf{F}_{net} \) on the dipole is the vector sum of the forces on the two charges:
\[ \mathbf{F}_{net} = \mathbf{F}_+ + \mathbf{F}_- = q \mathbf{E} - q \mathbf{E} = 0 \]
Thus, the net force on the dipole in a uniform electric field is zero.

**Hint**: In a uniform electric field, the forces on the dipole's charges cancel each other out.

4. **Analyzing the Torque**:
The torque \( \tau \) acting on the dipole about the center of the dipole can be calculated using the formula:
\[ \tau = \mathbf{p} \times \mathbf{E} \]
The magnitude of the torque can also be expressed as:
\[ \tau = pE \sin \theta \]
where \( \theta \) is the angle between the dipole moment vector \( \mathbf{p} \) and the electric field vector \( \mathbf{E} \).

**Hint**: The torque depends on the angle between the dipole moment and the electric field.

5. **Evaluating the Torque**:
- If \( \theta = 0^\circ \) (dipole aligned with the field), then \( \tau = 0 \).
- If \( \theta = 180^\circ \) (dipole anti-aligned with the field), then \( \tau = 0 \).
- For any other angle \( 0 < \theta < 180 \), the torque will be non-zero.

**Hint**: The torque is maximum when the dipole is perpendicular to the electric field (i.e., \( \theta = 90^\circ \)).

6. **Conclusion**:
From the analysis, we conclude:
- The net force \( F \) on the dipole in a uniform electric field is zero.
- The torque \( \tau \) can be zero or non-zero depending on the orientation of the dipole with respect to the electric field.

### Final Answer:
- **Force \( F \) must be zero**.
- **Torque \( \tau \) may be non-zero** depending on the orientation of the dipole.