Electric/electrostatic forces and magnetic forces of atoms and molecules


> On Moment

What is moment in physics?


In physics, moment is a combination of a physical quantity and a distance.





> On Dipole Moment


Dipole moment may refer to:





> On Momentum

Please refer to "Motion in Macrocosm"



Momentum is a quantity which is used for measuring the motion of an object. An object's momentum is directly related to the object's mass and velocity.


Linear momentum



Angular or rotational momentum


The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity.

L= I * ω

The above relationship can be transformed (https://en.wikipedia.org/wiki/Angular_momentum) as follows:

L= r * p

This is the cross product of the position vector r and the linear momentum p=mv of the particle.



> The Structure of the Atom



The quantum mechanical model of the atom

Quantum numbers



As mentioned in the above video from Khan Academy, in the Bohr model of the hydrogen atom, the electron is in orbit around the nucleus. In the quantum mechanics version of the model, we don't know exactly where the electron is but we can say with high probability that it is in an orbital. An orbital is the region of space where the electron is most likely to be found. It is also called an electronic shell or shell.


The shells are represented by the Principal quantum number (n). This takes only positive integer values: n=1, 2, 3...


Similarly to an object that perfoms a rotational motion, each electron is characterized by an angular momentum L. This is the cross product r*p where r is the distance from the nucleus and p is the particle's linear momentum (v*m). The orbital angular momentum L of en electron unlike that of a classic particle is quantized. We can find the quantized (allowed) values by solving Schrödinger’s equation. The L is associated to the orbital angular momentum quantum number or Azimuthal quantum number  (ℓ).



An orbiting charged particle sets up the magnetic field of a magnetic dipole, (Halliday-Resnick, Chapter 40 citing module 32-5).  The dipole moment is related to the angular momentum of the classical particle by:


{\boldsymbol {\mu }}={\frac {-e}{2m_{\text{e}}}}\,\mathbf {L} .


This is also quantized and is associated to the magnetic quantum number (ml). As mentioned in wikipedia since an electron has a magnetic moment, in the presence of a magnetic field, it will be subject to a torque which tends to make the vector L parallel to the field.  



An object rotates around an axis and if this axis passes through the body's center of mass then the object is said to rotate upon itself or spin. Although scientists say that the electron does not spin, it has an intrinsic property that made scientists choose this term. The scientists have named it spin angular momentum S, or simply spin. It is associated with the Spin quantum number (ms).


As also mentioned in wikipedia, the magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field (the Zeeman effect) — hence the name magnetic quantum number. However, the actual magnetic dipole moment of an electron in an atomic orbital arrives not only from the electron angular momentum, but also from the electron spin, expressed in the spin quantum number.


For the above reasons we define a total angular momentum which is the sum of the orbital and spin angular momenta.


If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is:



This is represented by the total angular momentum quantum number.




> Electric charge moving in an electric and a magnetic field


Electric charge moving in an electric (electrostatic) field (velocity being perpendicular to its field lines)





Electric charge moving in a magnetic field (velocity being perpendicular to its field lines)


Lorentz force F acts as centripital force and the charge will do a circular motion:

F=Fc <=> qvB=mv2/R <=> R=mv/qB


The radius of the circular motion, termed gyroradius, Larmor radius, or cyclotron radius is given by the above equation.


The angular frequency of this circular motion is known as the gyrofrequency, or cyclotron frequency, and can be expressed as




Applications : Cyclotron, Mass Spectrometer


Electric charge moving in an electric and a magnetic field experiences the Lorentz force.








> Gyromagnetic ratio and Larmor precession

Excerpts from wikipedia:


In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma.


Gyromagnetic ratio and Larmor precession

Main article: Larmor precession

Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus, or an electron, when placed in an external magnetic field B (measured in teslas) that is not aligned with its magnetic moment, will precess at a frequency f (measured in hertz), that is proportional to the external field:





Gyromagnetic ratio for an isolated electron 



Gyromagnetic ratio for a nucleus

The gyromagnetic ratio of a nucleus plays a role in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins precession in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon, the sign of γ determines the sense (clockwise vs counterclockwise) of precession.


Most common nuclei such as 1H and 13C have positive gyromagnetic ratios.[7][8] Approximate values for some common nuclei are given in the table below.[9][10]



(MHz T −1)





































Larmor precession







Electric/Electrostatic force on shared electron (pair) between two atoms – Covalent bond


Two atoms share an electron as they attract it with comparable electric (electrostatic) force – Electron attributed to both – Shared force/electrostatic interaction on electrons is termed a covalent bond


Hydrogen is the element with atomic number 1, which means it has one proton in its nucleus.

It has one electron in its outer shell. In order to form a stable outer shell that has two electrons, it needs another electron.


Fluorine is the element with the atomic number 9, which means it has nine protons in its nucleus.

It has two electrons in its first shell and seven in its outer shell. In order to form a stable outer shell that has eight electrons, it needs one electron.


A hydrogen atom will share its electron with a fluorine atom and in this way they both complete their outer shell. The electrons will be attracted by both nuclei via an electric force, an electrostatic force. How does that work out in space? Will the shared electrons be in the middle of the distance between the atomic centers? It depends on the strength of the electric force from each side.


The nucleus of fluorine with its 9 protons (positive charges) exerts a much more significant electric force on the electrons than the one-proton hydrogen nucleus. (We say that F is more electronegative than H).


As a result, the shared electrons will shift slightly towards the fluorine.


That means that in the HF molecule, the H side will have a proton on its own and a little further away there will be 9 protons and 10 electrons towards the F side. Therefore, the H side will be slightly positive and the F side with 10-9=1 electrons in surplus will have a negative charge.



Image location


Water or H20, constitutes a similar case.


Oxygen is the element with atomic number 8. It has 6 electrons in its outer cell and needs another two.


Two hydrogen atoms will share their electrons. The nucleus of oxygen (8 protons) exerts a much stronger electric force on the electrons than the one-proton hydrogen nucleus. As a result, the shared electrons will shift slightly towards the oxygen.






Electric/Electrostatic force between opposite charged ions - Ionic bond


Two atoms exchange an electron– Atoms are no longer electrically neutral but they become ions – Electrostatic interaction between ions is termed an ionic bond


Sodium is the element with atomic number 11, which means it has eleven protons in its nucleus.

It needs to discard one electron to form a stable outer shell of 8 electrons.

As mentioned, fluorine needs for the same reason one electron.

Sodium gives one electron and becomes a positively charged ion while fluorine gets one and becomes negatively charged. Opposites attract and we say that an ionic bond is formed between the two. The sodium chloride crystal is said to be ionically bonded.





Van des Waals forces : Electric/Electrostatic forces between dipoles (permanent or induced)




Electric/Electrostatic force between permanent dipoles (Keesom force)

We mentioned that the molecules of water and HF are dipoles. The (+) pole of one molecule attracts the (–) pole of the other. Generally, we expect that the hydrogen atom in all its interactions with strong electronegative atoms e.g. N, O, F will have its electron shifted away and will thereby generate a dipole.


Electric/Electrostatic force between permanent dipole and corresponding induced dipole (Debye force)

One example of an induction-interaction between permanent dipole and induced dipole is the interaction between HCl and Ar. In this system, Ar experiences a dipole as its electrons are attracted (to the H side of HCl) or repelled (from the Cl side) by HCl.[6][7] 



Electric/Electrostatic force between instantaneously induced dipoles generated by electron cloud fluctuations (London dispersion force)


From this wikipedia link:


"The third and dominant contribution is the dispersion or London force (fluctuating dipole-induced dipole), which arises due to the non-zero instantaneous dipole moments of all atoms and molecules. Such polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in non-polar molecules. Thus, London interactions are caused by random fluctuations of electron density in an electron cloud. An atom with a large number of electrons will have a greater associated London force than an atom with fewer electrons. The dispersion (London) force is the most important component because all materials are polarizable, whereas Keesom and Debye forces require permanent dipoles. The London interaction is universal and is present in atom-atom interactions as well. For various reasons, London interactions (dispersion) have been considered relevant for interactions between macroscopic bodies in condensed systems.Hamaker developed the theory of van der Waals between macroscopic bodies in 1937 and showed that the additivity of these interactions renders them considerably more long-range.[4]"