In which of the following cases,force acting on the dipole could be zero

Options

A.
B.
C.
D. None

Answer

To determine in which case the force acting on an electric dipole could be zero, we need to analyze the scenarios based on the electric field and the dipole's orientation. An electric dipole consists of two equal and opposite charges separated by a small distance.

### Step-by-Step Solution:

1. **Understanding the Dipole**:
- A dipole consists of a positive charge (+q) and a negative charge (-q) separated by a distance 'd'.
- The dipole moment \( p \) is defined as \( p = q \cdot d \).

2. **Electric Field Intensity**:
- The electric field intensity \( E \) at any point in space is related to the density of electric lines of force. The greater the density of lines, the stronger the electric field.

3. **Analyzing the First Case**:
- In the first scenario, the dipole is placed in a non-uniform electric field where the density of electric lines of force is greater on one side than the other.
- This results in unequal forces acting on the two charges of the dipole. Therefore, the net force on the dipole is not zero.

4. **Analyzing the Second Case**:
- In the second scenario, the dipole is placed in a uniform electric field, but the forces acting on the charges are equal in magnitude but opposite in direction.
- Although the forces are equal, they do not cancel each other out completely because they act in different directions. Thus, the net force is not zero.

5. **Analyzing the Third Case**:
- In the third scenario, the dipole is placed in a uniform electric field where the density of electric lines of force is the same on both sides of the dipole.
- Here, the forces acting on both charges are equal in magnitude and opposite in direction. Therefore, the net force acting on the dipole is zero.

### Conclusion:
The correct scenario in which the force acting on the dipole could be zero is the **third case** where the dipole is in a uniform electric field with equal electric field intensity on both sides.