Point `P` lies on the axis of a dipole . If the dipole is rotated by ` 90^@` anti-clock wise , the electric field vector ` vec E` at `P` will rotate by .

Options

A. `90^(@)` clockwise
B. `180^(@)` clockwise
C. `90^(@)` anticlockwise
D. `180^(@)` anticlockwise

Answer

To solve the problem step by step, we need to analyze the situation involving an electric dipole and the effect of rotating it on the electric field at a point on its axis.

### 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 \( \vec{p} \) is defined as \( \vec{p} = Q \cdot \vec{d} \), where \( \vec{d} \) is the vector pointing from the negative charge to the positive charge.

2. **Identifying the Point P**:
- Point P lies on the axis of the dipole. The electric field \( \vec{E} \) at point P due to the dipole can be calculated using the formula for the electric field along the axial line:
\[ \vec{E} = \frac{2kp}{r^3} \]
where \( k \) is the Coulomb's constant, \( p \) is the dipole moment, and \( r \) is the distance from the center of the dipole to point P.

3. **Initial Orientation of the Dipole**:
- Initially, the dipole is oriented such that the dipole moment \( \vec{p} \) points towards point P. Therefore, the electric field \( \vec{E} \) at point P is directed along the dipole moment.

4. **Rotating the Dipole**:
- When the dipole is rotated 90 degrees anti-clockwise, the orientation of the dipole moment changes. The new orientation of the dipole moment will now be perpendicular to its original position.

5. **Effect on the Electric Field**:
- After the rotation, the electric field at point P will also change. The electric field at point P will now be directed tangentially to the dipole's new orientation.

6. **Determining the Angle of Rotation of the Electric Field**:
- The initial electric field was radial (along the dipole moment), and after the rotation, it becomes tangential. This means that the electric field vector has rotated from its original direction to a new direction that is 90 degrees away from the original.

7. **Conclusion**:
- Therefore, the electric field vector \( \vec{E} \) at point P will rotate by 90 degrees as well when the dipole is rotated by 90 degrees anti-clockwise.

### Final Answer:
The electric field vector \( \vec{E} \) at point P will rotate by **90 degrees**.