The electric field on axial line due to an electric dipole at a distance from its centre position is E. If the dipole is rotated through an angle of 90° about its perpendicular axis, electric field at the same point will be

Explanation:

1. Electric field on the axial line of a dipole

The electric field E due to a dipole at a point on its axial line (along the line passing through both charges) is given by:

E = (1 / (4πε₀)) * (2p / r³)

Where:

• p is the dipole moment,
• r is the distance from the dipole to the point where the field is being calculated.

2. Effect of rotating the dipole

If the dipole is rotated about its perpendicular axis by an angle of 90°, the relative orientation of the dipole moment with respect to the point where the electric field is calculated changes.

• Initially, when the dipole is aligned along the axial line, the field at the point is maximized.
• After rotating the dipole by 90°, the dipole moment becomes perpendicular to the axial line, so the electric field at that point decreases.

3. New electric field:

The electric field on the axial line is proportional to the cosine of the angle between the dipole moment and the line connecting the dipole to the point where the field is calculated. Initially, the angle is 0° (cos(0°) = 1), so the field is E. After the dipole is rotated by 90°, the angle between the dipole moment and the point is 90° (cos(90°) = 0), which results in the electric field becoming weaker.

The electric field at the same point after the rotation is E/2 because the dipole’s field decreases in this configuration.

Final Answer

The electric field after rotating the dipole by 90° is E/2.