Electrostatic dipole:
Electrostatic dipole consists of a pair of equal and opposite point charges separated by a very small distance. Example: H2O, NH3 etc.
 Electrostatic dipole moment of an electric dipole is defined as the product of the magnitude of either charge of the dipole and the dipole length. If +q and –q are the two charges are separated by distance 2l then dipole moment 
 = q2l and the direction is from –q charge to +q charge. SI unit is Cm and dimension is [LTA].
Electric field intensity at a point on the axis of a dipole:
Let us consider an electric dipole consists of -q and +q at points A and B respectively separated by a distance 2a. O is the midpoint of the dipole and the dipole moment is = q2a
. To calculate electric field at a point P on the axis of the dipole, at a distance r from O we consider a unit + ve test charge is placed at P.
The electric field intensity at point P due to –q charge is E1 = 
= 
 direction is 
.
The electric field intensity at point P due to +q charge is E2 = 
= 
direction is 
.
If E is the resultant electric field intensity at point P, then E = E2 – E1 (direction is 
)
E = –
Or, E = kq[
]
Or, E = 
Â
E = 
Where k = 
so, E = 
If r>>2a then, 
 = 
 .
Electric field intensity at a point on the equatorial line of a dipole: Â
Let us consider an electric dipole consists of -q and +q at points A and B respectively separated by a distance 2a. O is the midpoint of the dipole and the dipole moment is = q2a. To calculate electric field at a point P on the equatorial line of the dipole, at a distance r from O we consider a unit + ve test charge placed at P.
The electric field intensity at point P due to –q charge is E1 =  = 
 direction is 
.
The electric field intensity at point P due to +q charge is E2 = = Â direction is 
.
So, E1 = E2 =
The components of 
and 
along the equatorial line are respectively E1
 and E2 cancelled due to equal in magnitude and opposite in direction. The components of and  perpendicular to the equatorial line are respectively E1
 and E2 provide the net electric field E at point P.
E = E1cosθ + E2cosθÂ
Or, E = 
Or, E = 
E = 
Where k = so, E = 
If r >>2a then, = 
. Â
Torque acting due to a dipole placed in uniform electric field:
Let us consider an electric dipole consists of -q and +q charge at points A and B respectively separated by a distance a is placed in the electric field of intensity E at an angle θ. The dipole moment is = qa.
Force acting on charge –q at A is 
= –
and the force acting on charge +q at B is 
= . Since forces and are equal and oppositely directed, they form a couple.
The magnitude of moment of the couple i.e. torque (
) is given by,
= magnitude of either force 
 arm of the couple
= qE BC = qE asinθ = qaEsinθ = pEsinθ
 = .
Concept of dipole moment:
Three charges +q, +q, and -2q are placed at the vertices of an isosceles triangle where the lines joining -2q with +q and +q respectively create angle θ. What is the dipole moment of the system?
One –q and one +q charge form one dipole with dipole moment P (= ql where l is the distance between –q and + q).
Similarly, another –q and +q charge form one dipole with dipole moment P.
So, the net dipole moment P/ = 
Click the button to go to the next part of this chapter.
Click the button to go to the previous part of this chapter.