Electric field intensity at a point on the broad side-on position equatorial line:

Consider an electric dipole consisting of two equal but opposite charges -q and +q separated by a vector distance of 2l.

Let P be a point at a distance r from the center of the dipole O.

The electric intensity at P due to the dipole is the vector sum of the field due to the charge -q at A and +q at B.

The resultant intensity is the vector sum of EA and EB.

EA and EB can be resolved into two components.

The y-components of the field cancel each other because,

EA sin straight theta = EB sin straight theta, oppositely directed.
The x components add up to give the resultant field E.

The magnitude of E is,

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