Coulomb force law

The experimental observations of Coulomb on electric forces are summarized in the Coulomb force law ... 

The success of the Debye-Hlickel limiting law is no mean achievement. One has only to think of the complex nature of the real system, of the presence of the solvent, which has been recognized only through a dielectric constant, of the simplicity of the Coulomb force law used, and, finally, of the fact that the ions are not point charges, to realize (Table 3.7) that the simple ionic cloud model has been brilliantly successful—almost unexpectedly so. It has grasped the essential truth about electrolytic... 

The second obvious correction takes account of the mutual electrostatic repulsion of the protons. According to the Coulomb force law, the mutual electrostatic potential energy of two protons, each having a charge of e coulombs, separated by a distance r, is proportional to e jr. To a reasonable approximation, we may consider each of the Z protons as interacting with a total of (Z — 1) other protons, at an average distance equal to r, the radius of... 

We begin with the force between two point charges, q and qi, separated by a distance x in a vacuum from Coulomb s law... 

If two oppositely charged plates exist in a vacuum, there is a certain force of attraction between them, as stated by Coulomb s law ... 

Coulomb s law. This relationship poses no particular difficulties as a qualitative statement the problem arises when we attempt to calculate something with it, since the proportionality constant depends on the choice of units. In the cgs system of units, the electrostatic unit of charge is defined to produce a force of 1 dyne when two such charges are separated by a distance of 1 cm. In the cgs system the proportionality factor in Coulomb s law is unity and is dimensionless. For charges under vacuum we write... 

Since an electric field E in space is defined as the force experienced by a unit test charge q (strictly, in the limit of q -> 0), it follows that the field produced by qj is obtained by letting qj = qj = 1 in Coulomb s law ... 

Adsorption Forces. Coulomb s law allows calculations of the electrostatic potential resulting from a charge distribution, and of the potential energy of interaction between different charge distributions. Various elaborate computations are possible to calculate the potential energy of interaction between point charges, distributed charges, etc. See reference 2 for a detailed introduction. 

EIectrosta.tlcs. Electrostatic interactions, such as salt bridges, result from the electrostatic attraction that occurs between oppositely charged molecules. These usually involve a single cation, eg, the side chain of Lys or Arg, or the amino terminus, etc, interacting with a single anion, eg, the side chain of Glu or Asp, or the carboxyl terminus, etc. This attractive force is iaversely proportional to the distance between the charges and the dielectric constant of the solvent, as described by Coulomb s law. 

The only problem with the foregoing approach to molecular interactions is that the accurate solution of Schrddinger s equation is possible only for very small systems, due to the limitations in current algorithms and computer power. Eor systems of biological interest, molecular interactions must be approximated by the use of empirical force fields made up of parametrized tenns, most of which bear no recognizable relation to Coulomb s law. Nonetheless the force fields in use today all include tenns describing electrostatic interactions. This is due at least in part to the following facts. 

The force of attraction, calculated from Coulomb s law, for a uniformly charged, spherical, particle in contact with a grounded, conducting substrate is simply... 

In the derivation of the Boltzmann equation, it was noted that the distribution function must not change significantly in times of the order of a collision time, nor in distances of the order of the maximum range of the interparticle force. For the usual interatomic force laws (but not the Coulomb force, which is of importance in ionized gases), this distance is less than about 10 T cm the corresponding collision times, which are of the order of the force range divided by a characteristic particle velocity (of the order of 10 cm/sec for hydrogen at 300° C), is about 10 12 seconds. 

Certain negative ions such as Cl , Br, CNS , N03 and SO2 show an adsorption affinity to the mercury surface so in case (a), where the overall potential of the dme is zero, the anions transfer the electrons from the Hg surface towards the inside of the drop, so that the resulting positive charges along the surface will form an electric double layer with the anions adsorbed from the solution. Because according to Coulomb s law similar charges repel one another, a repulsive force results that counteracts the Hg surface tension, so that the apparent crHg value is lowered. 

Section 3.3.4 pointed out that cosolvents alter aqueous ionization constants as the dielectric constant of the mixture decreases, acids appear to have higher pKa values and bases appear (to a lesser extent than acids) to have lower values. A lower dielectric constant implies that the force between charged species increases, according to Coulomb s law. The equilibrium reaction in Eq. (3.1) is shifted to the left in a decreased dielectric medium, which is the same as saying that pKa increases. Numerous studies indicate that the dielectric constant in the region of the polar head groups of phospholipids is 32, the same as the value of methanol. [381,446-453] Table 5.2 summarizes many of the results. 

Tbginteraction between the two particles in this system is described by Coulomb s law, in which the force is proportional to the inverse-square of the distance between the particles and —e2 is the product of the charges on the electron and the proton. The corresponding potential function is then of the form... 

The first two terms on the right-hand side of Eq. (83) are usually assumed to be harmonic, as given for example by Eq. (6-74). The third term is often developed in a Fourier series, as given by Eq. (82). The potential function appropriate to the interaction between nonbonded atoms is taken to be of the Lennard-Jones type (Section 6.7.3). In all of these cases the necessary force constants are estimated by comparing the results obtained from a large number of similar molecules. If electrostatic interactions are to be considered, effective atomic charges must be suggested and Coulomb s law applied directly [see Eq. (6-81)]. 

In order to arrive at a mathematical relationship to describe London forces, we will use an intuitive approach. First, the ability of the electrons to be moved within the molecule is involved. Atoms or molecules in which the electrons are highly localized cannot have instantaneous dipoles of any great magnitude induced in them. A measure of the ability of electrons in a molecule to be shifted is known as the electronic polarizability, a. In fact, each of the interacting molecules has a polarizability, so the energy arising from London forces, Ei, is proportional to a2. London forces are important only at short distances, which means that the distance of separation is in the denominator of the equation. In fact, unlike Coulomb s law, which has r2 in the denominator, the expression for London forces involves r6. Therefore, the energy of interaction as a result of London forces is expressed as... 

From Bohr s postulates, it is possible to derive the energies of the possible stationary states responsible for the radiation that is absorbed or emitted by an atom consisting of a single electron and nucleus. The specification of these states permits one to then compute the frequency of the associated electromagnetic radiation. To begin, one assumes the charge on the nucleus to be Z times the fundamental electronic charge, e, and that Coulomb s law provides the attractive force, F, between the nucleus and electron ... 

Consider two stationary point charges, <2i and Q2, separated by a distance R. Let R be the distance vector from Q to Q2. Then Coulomb s law states that the electrostatic force F exerted upon Q2 by <2i is... 

Fe3+. There are several ways of defining electronegativity, the simplest being that of Allred and Rochow (1958), which calculates the force experienced by the outer electron from the nucleus using Coulomb s law of electrical attraction ... 

However, the recent developments in non-equilibrium statistical mechanics, and the success of its application in another field of physics where the long-range Coulomb forces play a major role, namely plasma physics, have led various authors to investigate the limiting laws for transport phenomena in electrolytes from a... 

Coulombic Force Coulomb s law of electrostatic force is written, in SI units, as... 

The value of the ionic dissociation constant for a given equilibrium is strongly influenced by the dielectric constant (e) of the medium according to Coulomb s law the force acting between the charged particles et + and e2 increases with decreasing e values ... 

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