Electric Dipole

An electric dipole is an arrangement of electric charges. Let’s say if one charge is negative then the other needs to be positive, provided that these two charges are of equal magnitude. Also, there should be a certain distance between these two charges.

Let’s suppose + q  and - q are the two charges separated by a distance ‘2a’, now joining the centre of these charges with a line, as shown below:

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The mid-point of this line is the centre of the dipole. The dipole has a certain length and also the moment.

Here, we are going to discuss electric dipole and dipole moment.

What is Electric Dipole and Electric Dipole Moment?

We understood that an electric dipole is an arrangement of equal and opposite charges. Since the two charges are separated by a distance ‘2a’, which is called the dipole length. The distance between the charge and the centre of the dipole is ‘a’.

So, what is an electric dipole moment?

The dipole moment is a vector quantity and is denoted by a symbol \[\overrightarrow{p}\]. Its magnitude is equal to the magnitude of either of the two charges. Since we don’t specify the sign for the dipole moment, we multiply either of the two charges with the dipole length. It is given by:

                            \[\overrightarrow{p} = q \overrightarrow{d}\] ….(1)

Here, d  = 2a, so, we can rewrite the equation as:

                               \[\overrightarrow{p} = q(2a)\] …..(2)

So, equation (2) is the magnitude of the dipole moment.

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So, what is the SI unit of the dipole moment?

We know that the unit of the charge is ‘C’ and that of distance is ‘m’. So, the unit of the dipole moment becomes:

Can we see the difference in equations (1) & (2)?

Yes, there is a big difference between the two, but how, let’s understand this:

See, in equation (1), we considered the distance ‘d’ as a vector quantity, however, in equation (2), both the quantities viz: charge and distance or dipole length are the scalar quantities. 

Now, when the product on the R.H.S of eq (2) are scalar, so, how can dipole moment be a vector quantity?  Yes, p can be a vector quantity only when we somehow convert the distance ‘2a’ as the displacement.

So, how can a distance be displaced, as these two quantities are different?

Now, let’s look at the following arrangement:

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When we take ‘2a’ displacement of the charge - q with respect to charge + q, .i.e., from L.H.S to R.H.S or of the charge + q with respect to charge - q (from R.H.S to L.H.S). Now, this  ‘2a’ becomes a vector quantity. Hence, equation (2) becomes:

                              \[\overrightarrow{p} = q(2 \overrightarrow{a})\]…..(3)

Or,                        \[|\overrightarrow{p}| = q \times (2a)\] …..(4)

So, what do you mean by electric dipole moment?

From eq (3), we define electric dipole moment as the product of charge and the displacement of + q charge with respect to - q charge.

Sometimes confusion arises in considering the direction of electric dipole moment. In Chemistry, we consider the displacement of + q charge with respect to charge - q, i.e., from right-to-left, while in Physics, we take the displacement of - q w.r.t. + q, i.e., from left-to-right.

There are two more units of the dipole moment, possessing a relationship between each. These are:

• StatC . cm 

• Debye (D) 

Also, 1 D = 10^-18 StatC . cm, which is approximately  = 3.33564 x 10^-30 C.m.

There’s something ideal included in the concept of dipole moment, let’s discuss it.

What is an Ideal Electric Dipole?

From eq (4): If the charge ‘q’ gets larger, the distance between the two charges becomes smaller and smaller,  to keep the product of these two quantities viz: ‘q’ and ‘2a’ as constant, i.e., \[\overrightarrow{p}| = q \times (2a)\] = constant, this is what we call it as an ideal dipole or point dipole.

Therefore, an ideal dipole is the smallest dipole having almost no size.

Significance of Electric Dipoles

We can find the application of electric dipoles in atoms and molecules, but how?

Consider one atom of Hydrogen and the other two of Oxygen in the water molecule. Now, what happens here is, a covalent bond forms between H and two O-atoms, and they come close to each other.

Since there is a difference in the electronegativity of H and O, there is a shift of charges; also, the centres of these atoms don’t coincide.

O is an electronegative element and a shared pair of electrons between H and O towards O. Therefore, the centre of the negative charge shifts towards O, and the positive one to the H-atom; also, a partial positive and the negative charge develops on H and O-atom, respectively. Now, the arrangement of H and O in the water molecule behaves like a dipole.

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