Derivation of electric field intensity of a diapole at point of equatorial plane

The derivation of the field intensity in the dipole at the point of equatorial plane is the result of the horizontal line.

Explanation:

The equatorial line of an axis on dipole is define as the line is perpendicular at the axial line and to pass from the mid way between the charges at both the poles.

The result of this intensity is the vector sum of the intensities with the PA and PB. The line EA and The line EB can be resolved into horizontal and the vertical components.

The vertical components of dipole cancel to each other because they both equally or opposite directed.

The horizontal line up gives the result of the dipole at the point of the equatorial.