Electric Field: Electric Dipole

Let an electric dipole is taken which constitutes (+q) and (- q) charge separated by the distance 2l.

Let from the mid point of the dipole at a distance ‘r’ is the point P at intensities due to (+q) and (-q) charge respectively.

direction along the dipole axis. 
E₂ =  direction opposite to the dipole axis. 
Resultant electric field intensity E = E₁ - E₂
  

B.

Electric lines of dipole.

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 2l. Let P be a point at a distance r from the centre 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.

Electric intensity at P due to - q = E_A = 
But    AP² = r² +l²;    
where AO = OB = l
Magnitude of E_A is |E_A| = 




The resultant intensity is the vector sum of.
E_A and E_B can be resolved into two components.
The y-components of the fields cancel each other because E_A sin θ = E_B sin θ and they are oppositely directed. The x-components add up to give the resultant field E.
 
E is directed along PC.
The direction of E can be found out by drawing the line of force passing through the point P.
The direction of E at P is opposite to the direction of the dipole moment p . 
i.e., parallel to the line joining the two charges and directed from + q to - q.
Then, 


  
When r > > I, then l² is very small compared to r².
E_axial = 
From the above two equations for E_eq and E_axial we find that the electric intensity at an axial point is twice the electric intensity at a point on the equatorial position, lying at the same distance from the centre of the dipole.