Consider, a short electric dipole having dipole moment p. A point P is at a distance r from the centre O of the dipole such that the angle between p and OP is θ.
Now, P act as a point on the axial line for pCosθ component and act as a point on the equatorial line for pSinθ component. The electric fields at point P due to pCosθ and pSinθ are E1 and E2 respectively. Also, they are perpendicular to each other.
Now, net electric field at point P is -
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