What is the angle between the directions of electric field due to an electric dipole and its dipole moment at any :
(i) Axial p oint . (ii) Equatorial point .

Explanation

To solve the problem regarding the angle between the directions of the electric field due to an electric dipole and its dipole moment at axial and equatorial points, we can follow these steps:

### Step-by-Step Solution:

#### (i) Angle at Axial Point

1. **Understanding the Dipole Moment**: The dipole moment (\( \vec{p} \)) is defined as the vector pointing from the negative charge (-Q) to the positive charge (+Q). This direction is taken as the direction of the dipole moment.

2. **Electric Field at Axial Point**: At an axial point (along the line extending from the positive to the negative charge), the electric field (\( \vec{E} \)) due to the dipole is directed away from the positive charge and towards the negative charge.

3. **Direction of Electric Field**: Since the axial point is closer to the positive charge, the electric field direction is aligned with the dipole moment direction. Therefore, the angle between the electric field and the dipole moment at this point is \( 0^\circ \).

#### (ii) Angle at Equatorial Point

1. **Understanding the Equatorial Point**: An equatorial point is located on the perpendicular bisector of the dipole. Here, the distances from both charges are equal.

2. **Electric Field at Equatorial Point**: At the equatorial point, the electric fields due to the positive and negative charges are equal in magnitude but opposite in direction.

3. **Direction of Electric Field**: The electric field due to the positive charge points away from it, while the field due to the negative charge points towards it. As a result, these two electric fields cancel each other out in the direction perpendicular to the dipole moment.

4. **Angle Between Electric Field and Dipole Moment**: Since the electric field at the equatorial point is directed perpendicular to the dipole moment, the angle between the electric field and the dipole moment is \( 180^\circ \).

### Final Answers:
- (i) The angle at the axial point is \( 0^\circ \).
- (ii) The angle at the equatorial point is \( 180^\circ \).