Question

derive an expression for the electric field at a point on the axial/equatorial position of an electric Dipole?

Answer 1

By solving this we will get
Enet=KP/(r^2+a^2)^3/2
where p stands for electric dipole

Answer 2

The NCERT formula is correct if used with vector notation as the direction of electric dipole moment is from -q(negative charge) to +q(positive charge) and the resultant electric field at any point on equatorial line is in direction opposite to the electric dipole moment so negative sign is used. The other formula which does not include negative sign is applicable to calculate the magnitude(not direction) of electric field.