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Electric Dipole
The Electric dipole is defined as a system having two equal but opposite charges separated by a finite distance. Assume that -q and q are two charges with the same amount of energy but opposite directed. The electric dipole is the product of the charge q and the vector d (which has a direction from -q to q ), electric dipole is also known as electric dipole moment and can be expressed as the equation below:

p = qd

The electric field E caused by -q and q at the point P is:


If the dipole lies along the z-axis, then we have:
p = az · p = p(aR · cosθ - aθ · sinθ)

and
R · p = R · p · cosθ

Therefore we can express the electric field E as below:


The unit of electric dipole is coulomb · meter [Cm].

The total electric charge on an electric dipole is zero, but its electric filed is not zero, as the position of the two opposite charges is different. 

Calculation:
Example-1: An electric dipole is placed in an electric field of a point charge, then:
a)  torque acting on it may be zero
b)  torque acting on it may not be zero
c)  torque acting on it is always zero
d)  None of above

Reason: An electric dipole is placed in an electric field of a point charge, and the torque acting on it may be zero because electric dipole is having two equal and opposite charges. When two different forces act on them, the resultant force may become zero, and keeps the dipole moment in translational equilibrium. As the two forces have different lines of action, the dipole will experience a torque and it may be zero.

Example-2: The electric dipole moment of NaCl atom is 3.4 x 10-30 Cm. The charges on both atoms are unlike and of same magnitude. The distance between the charges is 0.1A, then the magnitude of this charge is?
a) 17 x 10-20 C
b) 68 x 10-20 C
c) 34 x 10-20 C
d) 34 x10-10 C

Reason:
We know that p = qd
p = 3.4 × 10-30
d = 0.1 A = 0.1 × 10-10 m
q = ?

p = qd
q = p / d
q = (3.4 × 10-30) / (0.1 × 10-10)
q = 3.4 × 10 × 10-20
q = 34 × 10-20 C

Example-3: An electric dipole is placed at the centre of a sphere. The flux passing through the surface of the sphere is?
a) Zero 
b) can not be zero
d) infinity
d) none of above

Reason: Answer is zero
An electric dipole is place at the centre of sphere, and so the total electric charge on sphere is zero. The flux is passing through the surface of the sphere and the flux linked with any surface is the surface integration of the electric field over the given surface. So, the flux of surface of the sphere is zero.



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