The electric field intensity due to the dipole at the point A on the axis of the dipole is given by
EA=2kpr3......(1)
where, p is electric dipole moment, r is the distance of point A from dipole and k=14πϵ0
The direction of the electric field E is along the axis of the dipole from the negative charge towards the positive charge.
Also, The electric field intensity due to the dipole at the point B on the perpendicular bisector of the dipole is given by
EB=kpr3......(2)
The direction of the electric field E is parallel to the axis of the dipole from the positive charge towards the negative charge.
Hence, direction of electric field intensity due to the dipole at the point A is opposite to that of at point B.(refer the figure)
From (1) and (2), we get
→EA=−2→EB