Electric Field at a Point on the Equatorial Line of an Electric Dipole
In figure, an electric dipole AB is shown. The charges at point A and B are -q and +q respectively and the distance between them is \(2\overrightarrow { \alpha }\). We have to calculate electric field intensity at point O.
Electric field at point P due to charge +q,
According to the figure the vertical components of E1 and E2 (E1 sinθ and E2 sinθ) gets cancel out due to in opposite direction and the horizontal components (E1 cosθ and E1 cosθ) are in same direction so they are added.
If the value of a2 is very smaller than r (a<<r), then a2 can be considered negligible as compared to r2
It is clear that equal distance r,
Eaxial = 2Eequatorial
Thus (i) the electric field intensity placed at axis is twice the electric field at point on the equatorial line of the electric dipole.
(ii) The direction of electric field at a point on the axial line of the dipole is in same direction whereas it is in opposite direction in case when the point is at equatorial line of the electric dipole.
It is clear that for both the cases (axial and equatorial), for distant points (r >> 2a), the electric field, E ∝ \(\frac{1}{r^3}\).
