Electric Dipole

Introduction

A system of two charges +q and -q, equal in magnitude and opposite in polarity segregated by a small distance '2a' is called an electric dipole. The electric dipole moment vector of this system is given as:

Images Coming soon

Where '2a' is the vector that joins the negative charge to the positive charge.

Electric Dipole

The SI unit of electric dipole moment is coulomb-meter(Cm). The electric dipole moment gives the measure of strength linked with the electric dipole.

The middle point of the line joining the two charges +q and –q is called the centre of the dipole. The line that is along the direction of dipole moment is called the axis of dipole.

Total amount of charge of an electric dipole is zero but the electric field due to dipole is not zero as they do not cancel out, instead they add up as the charges are segregated by some distance. But at larger distances (r>>>2a), the electric field due to charges +q and –q almost cancels out.

Physical Significance of Electric Dipole

Electric dipole moment also exists in chemistry like in physics. In chemistry, some of the molecules don’t have permanent dipole moment but it can be induced and others have permanent dipole moment irrespective of the presence of any external electric field. So the study of electric dipoles helps to understand the electrical behavior of mater and the alignment of dipole with external electric field. The centres of positive and negative charges in most molecules coincides and therefore, their dipole moment comes to be zero. But when the electric field is present, they can develop a dipole moment. These molecules are called as non-polar molecules and examples are $\mathrm{CO_2, CH_4}$ etc.

But in few molecules, the centre of positive and negative charges doesn't coincide which results in the presence of permanent dipole moment oriented in random directions. However, with the application of any external electric field, they align themselves with the direction of electric field and that material is said to be polarized. These molecules are called as polar molecules like $\mathrm{H_2O}$.

Images Coming soon

Electric field due to a dipole

The electric field due to dipole at any point can be calculated using the Coulomb's law and superposition principle.

On the axis of dipole

Let us consider a point M on the axis of dipole at a distance of x from the centre of the dipole near to the positive charge +q.

Let the electric field due to charge –q be E1 and electric field due to charge +q be $\mathrm{E_2}$.

The direction of dipole moment as we know will be from negative to positive charge.

The electric field due to charge –q,

The electric field due to charge +q,

As charge –q is at larger distance from point M, so the electric field due to charge –q will be less than that due to charge +q. So, the net electric field will be towards right of the point M.

So the net electric field,

For x>>>>a,

On the equatorial plane of dipole

In this case, let us consider a point Q on the perpendicular bisector of the line joining the two charges at a distance x from the centre of the dipole.

Let the electric field due to charge –q be $\mathrm{E_1}$ and the electric field due to charge +q be $\mathrm{E_2}$.

Let the distance between charge –q and point Q be r and same will be the distance between charge +q and point Q.

The electric field due to charge –q will be toward the charge and the electric field due to positive charge will be away from the charge.

The magnitude of electric field due to charge –q,

The magnitude of electric field due to charge +q,

The electric field $\mathrm{E_1}$ will have two components. Similarly, $\mathrm{E_2}$ will have two components.

The vertical components of electric fields will get cancelled out as the magnitude of $\mathrm{E_1}$ and $\mathrm{E_2}$ are same.

So, the net electric field E due to the dipole will be in the direction opposite to the direction of dipole moment.

Since

For x>>>>a,

So we can say that for x>>>a, electric field doesn't depend on q and a separately but it depends on the dipole moment or the product of q and a.

Conclusion

The magnitude and direction of electric field due to dipole not only depend on the distance x but also on the angle between position vector x and dipole moment p.

From the equations of electric field due to dipole, we can say that for larger distances, the magnitude of electric field on the axis of dipole is equal to times the magnitude of electric field on the equatorial plane.

FAQs

Q1. What is the SI unit of the dipole moment?

Ans. The SI unit of dipole moment is Coulomb-meter

Q2. On what factors, does the electric field due to dipole depend?

Ans. Electric field due to dipole depends on the distance on the point from the centre of dipole where we have to find the electric field and the angle between the position vector and the dipole moment.

Q3. Is the electric dipole moment a vector quantity?

Ans. The electric dipole moment is a vector quantity as it has both magnitude and direction.

Q4. What is the ratio of electric field due to dipole on the axis of dipole and on the equatorial plane of the dipole?

Ans. The ratio of electric field due to dipole on the axis of dipole and on the equatorial plane of the dipole is 2:1.

Q5. What is an electric dipole moment?

Ans. An electric dipole moment is defined as the product of magnitude of the charge and the distance between the two charges.