Electric dipole

The electric dipole is the simplest neutral electrical configuration that can be found in nature. Pure dipoles (not approximations) are composed of two electrical charges Q, of the same magnitude, but of opposite directions. In the same manner as for individual charges, the electric dipole also has field lines (of the electric field), which "enter" the negative charge and "come out" of the positive charge, as shown in photo 1. But what is the interest in the study of electric dipoles? It is important to understand them, because almost all the matter around us is electrically neutral (same amounts of positive and negative electrical charges), thus formed by dipoles. Do not understand dipole as a system formed exclusively by a proton and an electron-although these form a "pure" dipole - but rather as any charges whose characteristics have been listed above. Carbon monoxide (CO) is a good example; oxygen has a higher electronegativity than carbon, thus having a function analogous to that of negative electrical charge in a "pure" dipole (note that both carbon and oxygen are chemical elements and are therefore electrically neutral. It is the electronegativity that causes them to play roles similar to those of non-neutral electrical charges). But what is electronegativity? Basically it's the aptitude that an atomic nucleus possesses to attract electrons from a chemical bond. In the case of carbon monoxide the type of bonding is covalent, and there is therefore electron sharing. Finally, the fact that oxygen is more electronegative than carbon causes it to "pull" the electrons of the carbon's valence shell closer. As the negative charges (electrons) are closer to oxygen this is said to be the "negative pole" of the molecule, while carbon becomes the "positive pole". The presence of polarity ensures the classification of carbon monoxide as a "polar molecule".

Still not convinced of the importance of electric dipoles? The water molecule itself (H2O) is a model of electric dipole, and the conditions of the water is responsible for the formation of water (yes, it is the mechanism of water formation!). The same explanation of the polarity given to carbon monoxide is valid for water, but water is composed of 3 atoms (one oxygen of two hydrogens), and oxygen is again the most electronegative. In setting a model, it is considered that the water molecule consists of two simple electric dipoles, being 2 pairs of hydrogen-oxygen (note that they are still only 3 atoms, not 4!).

But how does dipole formation occur? What's the dynamics between dipoles? Consider four free electrical charges (randomly positioned), two positive and two negative. First a positive charge will attract a negative (according to Coulomb's law), forming a dipole. The same will happen for the other two electrical charges. We now have a system consisting of two dipoles. The dipoles, as mentioned, despite being electrically neutral, have an electric field. Therefore, the electric field of dipole 1 will act on dipole 2 and the electric field of dipole 2 will act on dipole 1, causing both dipoles, under the action of a torque, to undergo a rotation, making them align. The description given above is shown in photo 2.

There is an important relationship involving dipoles, called the electrical dipole moment. It is essentially a vector entity that "measures" the strength of an electric dipole. Its mathematical form is given according to photo 3. How can we interpret this mathematical definition? Why are we multiplying position vectors (rj) by scalars (charges)? In electromagnetism, a field of study in which electrostatics are contained, the use of coordination systems is widely applied (whether Cartesian, cylindrical or spherical coordinates). To calculate the electric dipole moment we need to define a system of coordinates; in our case, the Cartesian coordinates are shown to be the simple ones. We then need to define a point of origin for the adopted coordination system. The interesting thing is that, although the electric dipole moment explicitly depends on the position vector (vector that connects the origin of the system to the referred charge), it does not matter where we choose the point of origin, it can be chosen arbitrarily. As for how to interpret the moment of electric dipole, we can think of it, in a similar conceptual manner, as the center of mass. The center of mass is defined as the point in an object in which one can think (hypothetically) that all mass is contained there (given mathematically in photo 4). Note the similarity between the electric dipole moment and the center of mass. However, there is a fundamental difference. We do not divide ∑q (r) ⃗ by ∑q because the sum of all the charges of a dipole is equal to zero (because the dipoles are electrically neutral). If we were to make such a division we would be dividing an amount by zero, which has no physical sense and is a mathematical indefinition. The mentioned torque is given by: τ ⃗=p ⃗XE ⃗

Where p ⃗ is the electric dipole moment and E is the electric field applied in the dipole. Because it is a vector product, the direction of the resulting vector (τ )will make an angle of 90 degrees with the plane (if the plane is represented by the x and y axes, think that the torque will point in the direction of the z axis).

Electric dipoles are extremely important because they provide the explanation for various phenomena, underpinning all areas of science, including biology.

For instance, in the study water's polarity, we learn that, because the water is polar and the oil is non-polar (there is no dipole moment), these do not mix.

photo 1: Electric dipole

photo 2: Dynamic between electric dipoles

photo 3: Definition of electric dipole

photo 4: Definition of center of mass

Reference material:

MITx: 8.02.1x Electricity and Magnetism: Electrostatics

Elements of eletromagnetism ( Matthew N. O. Sadiku)