How Does An Electric Dipole Work

The concept of an electric dipole is pretty simple. The electric dipole is a pair of point charges equal in magnitude but carrying opposite charges separated by distance.

• +q and -q are point charges separated by a distance of 2x.
• The middle point of the charges +q and -q is the dipole’s centre. 
• The dipole is always measured from negative to positive charge direction.

Besides the electric dipole, there is the magnetic dipole in electromagnetism. A magnetic dipole is the closed motion of a system of electric current. 

What is the dipole moment?

Electric dipole moment is the dissociation of opposite charges within a system. It is used to measure the overall polarity of the system. The SI metric unit of electric dipole moment is coulomb-metre (C.m). Another unit that is used in atomic physics is debye (D).

Formula

The electric dipole moment is denoted by p. Let us assume the following:

• The point charges are +q and -q.
• The distance between them is 2x.

Thus, the formula of electric dipole moment will be-

p = q2x 

Electric dipole moment is a vector quantity. Its magnitude is the net charge of +q and -q, and the direction is from -q towards +q. 

The working mechanism of an electric dipole

To understand the working mechanism of an electric dipole, we need to conceptualise how an electric dipole behaves in an electric field. 

The field of an electric dipole for a point on the axial line

The electric field at P (Eii) due to the charge +q

The above diagram depicts the electric field lines of an electric dipole.

• P denotes a point on the axial field line AB where field intensity is to be measured. 
• The r is the distance between the centre of the dipole O and the point P. 
• Let Ei and Eii denote the electric field. 

Along the line BP: Eii = 1/4𝝅𝛆0 x q/(BP)2

Or, Eii = 1/4𝝅𝛆0 x q/(r-x)2  

The electric field at P (Ei) due to charge -q

Along the line PA: Ei = 1/4𝝅𝛆0 x q/(PA)2

Or, Ei = 1/4𝝅𝛆0 x q/(r+x)2  

Therefore, E at P = Eii – Ei

Or, E = 1/4𝝅𝛆0 x [q/(r-x)2 – q/(r+x)2]

Upon simplifying, E = q/4𝝅𝛆0 x 4xr/(r2-x2)2

Or, E = q2x/4𝝅𝛆0 x 2rx/(r2-x2)2

Now we know [p = q2x] and we assume a constant [k = 1/4𝝅𝛆0]

So, the final equation stands- E = 2kpr/(r2-x2)2 along BP. 

Now, if (2x<<<r) then E = 2kp/r3

Force of an electric dipole

The general formula of the force of an electric dipole is F = Eq, but there are two separate cases. To understand this topic, we will use another diagram.

• Case I

We placed an electric dipole in an electric field E. Because of the electric field, the positive charge will experience a force in the direction of the field, and the negative charge will experience a force in the opposite direction of the electric field.

Here, the net Force Fnet = 0 (as the forces are equal in magnitude).

• Case II

Here, position 3 of positive and negative charges reverse. So, instead of the forces facing each other, they are applied in opposite directions. But also, in this case, the net force Fnet = 0 (as the forces are equal in magnitude).

Torque

When an electric dipole is placed perpendicularly in an electric field, it experiences a torque.

In the above diagram, the positive and negative charges face a force F in the clockwise direction. As a result, the dipole experiences a torque at the centre. This torque can be calculated by: T net = T1 + T2

            Or, T net = Fx/2 + Fx/2 [ as torque T = Force x lever arm]

            Or, T net = Fx. 

If the electric dipole is placed at an angle inside the field, the formula changes.

T net = T1 + T2

Or, T net = Fx/2sinΘ + Fx/2sinΘ

Or, T net = FxsinΘ

Or, T net = EqxsinΘ [ F = Eq]

What are some examples of electric dipoles?

The examples of  electric dipoles include various molecules:

• A water molecule ( H2O)
• NH3

Conclusion

The electric dipole and electric dipole moment play an essential part in grasping the basics of electromagnetism. The various diagrams will make understanding this topic easier. Let us recap the main points of this topic. The electric dipole is simply two points of equal and opposite charges. Dipole moment is used to separate those point charges. The electric dipole has characteristics like force and torque when placed in an electric field. To get a better idea of the chapter, one should also read the magnetic dipole.