A dipole is kept near an infinite line of charge. If the net force on the dipole is zero, then its dipolse moment is

Options

A. parallel to the line of charge
B. along the perpendicular drawn from the dipole to the line of charge
C. along the normal to the plane formed by the above two lines
D. net force onn a dipole kept near an infinte line of charge can never be zero

Explanation

To solve the problem of a dipole placed near an infinite line of charge with the condition that the net force on the dipole is zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Dipole**: A dipole consists of two equal and opposite charges (let's say +q and -q) separated by a distance 'd'. The dipole moment (p) is defined as:
\[ \mathbf{p} = q \cdot \mathbf{d} \]
where \( \mathbf{d} \) is a vector pointing from the negative charge to the positive charge.

2. **Force on a Dipole in an Electric Field**: When a dipole is placed in an electric field \( \mathbf{E} \), it experiences a torque \( \tau \) given by:
\[ \tau = \mathbf{p} \times \mathbf{E} \]
and a net force \( \mathbf{F} \) which can be expressed as:
\[ \mathbf{F} = q \mathbf{E}_{+} - q \mathbf{E}_{-} \]
where \( \mathbf{E}_{+} \) is the field at the position of the positive charge and \( \mathbf{E}_{-} \) is the field at the position of the negative charge.

3. **Electric Field due to an Infinite Line of Charge**: The electric field \( \mathbf{E} \) due to an infinite line of charge with linear charge density \( \lambda \) at a distance \( r \) from the line is given by:
\[ \mathbf{E} = \frac{\lambda}{2\pi \epsilon_0 r} \]
This field points radially outward from the line of charge.

4. **Condition for Zero Net Force**: For the net force on the dipole to be zero, the forces acting on the positive and negative charges of the dipole must be equal in magnitude and opposite in direction. This occurs when the dipole is aligned such that the dipole moment \( \mathbf{p} \) is parallel to the electric field \( \mathbf{E} \) of the line charge.

5. **Conclusion**: Since the dipole moment must be parallel to the line of charge for the net force to be zero, we can conclude that the dipole moment is:
\[ \text{Dipole moment } \mathbf{p} \text{ is parallel to the line of charge.} \]

### Final Answer:
The dipole moment is parallel to the line of charge.