An electric dipole is kept in the electric field produced by a point charge

Options

A. dipole will experience a force
B. dipole will experience a torque
C. it is impossible to find a path ( not closed) in the field on which work required to move the dipole is zero.
D. dipole can be in stable equilibrium

Explanation

To solve the problem of an electric dipole placed in the electric field produced by a point charge, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Electric Field of a Point Charge**:
- A point charge \( Q \) creates an electric field \( \vec{E} \) that radiates outward from the charge. The electric field at a distance \( r \) from the charge is given by the formula:
\[ \vec{E} = \frac{kQ}{r^2} \hat{r} \]
where \( k \) is Coulomb's constant and \( \hat{r} \) is the unit vector pointing away from the charge.

**Hint**: Remember that the direction of the electric field is determined by the nature of the charge (positive or negative).

2. **Defining the Electric Dipole**:
- An electric dipole consists of two equal and opposite charges, \( +q \) and \( -q \), separated by a distance \( d \). The dipole moment \( \vec{p} \) is defined as:
\[ \vec{p} = q \cdot \vec{d} \]
where \( \vec{d} \) is a vector pointing from the negative charge to the positive charge.

**Hint**: The dipole moment gives an idea of the strength and orientation of the dipole in the electric field.

3. **Placement of the Dipole in the Electric Field**:
- When the dipole is placed in the electric field of the point charge, the positive charge \( +q \) will experience a force in the direction of the electric field, while the negative charge \( -q \) will experience a force in the opposite direction.

**Hint**: Analyze the forces acting on each charge of the dipole separately.

4. **Calculating the Net Force on the Dipole**:
- The force on the positive charge is:
\[ \vec{F}_{+} = +q \vec{E} \]
- The force on the negative charge is:
\[ \vec{F}_{-} = -q \vec{E} \]
- The net force \( \vec{F}_{net} \) acting on the dipole is the vector sum of these forces:
\[ \vec{F}_{net} = \vec{F}_{+} + \vec{F}_{-} = +q \vec{E} - q \vec{E} = 0 \]
- However, since the forces are equal in magnitude and opposite in direction, they create a torque about the center of the dipole.

**Hint**: Consider the effect of the separation between the charges on the torque experienced by the dipole.

5. **Torque on the Dipole**:
- The torque \( \tau \) experienced by the dipole in an electric field is given by:
\[ \tau = \vec{p} \times \vec{E} \]
- If the dipole is not aligned with the electric field, it will experience a torque that tends to align it with the field.

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

6. **Equilibrium of the Dipole**:
- The dipole can be in stable equilibrium when it is aligned with the electric field. If it is not aligned, it will experience a torque that will try to align it, indicating that it is not in stable equilibrium.

**Hint**: Think about the conditions under which the dipole would remain in equilibrium.

### Conclusion:
Based on the analysis:
- The dipole experiences a force due to the electric field of the point charge.
- The dipole does not experience a torque if it is aligned with the field.
- It can be in stable equilibrium when aligned with the field.

### Final Answer:
The correct statement is that the dipole will experience a force in the electric field produced by the point charge.