Electrostatic potential energy, electrically

Since /(r) is the electrostatic potential energy per unit charge, the gradient of this parameter with distance must be equal to the force acting on a unit charge - which is the definition of the electric field. Hence it follows that... 

Estimated electric field (surface) 2 x 1013 to 1015 V/m Estimated magnetic field (surface) 106 Tesla Electrostatic potential energy (for 1 mm size) 33 J... 

If a charge distribution p(r) is placed in an electric field [(r)] due to a second nonoverlapping charge distribution, p (r), the electrostatic potential energy of the system is given by... 

In the absence of an electric field the charged vacancy migrates randomly, and its mobility depends on temperature since this determines the ease with which the Na+ surmounts the energy barrier to movement. Because the crystal is highly ionic in character the barrier is electrostatic in origin, and the ion in its normal lattice position is in an electrostatic potential energy well (Fig. 2.17). 

Here, and p are the electric potentials in the metal, in the bulk solution and at the inner Helmholtz plane, x = / rw max is the surface concentration of the adsorbed water molecules in the absence of chemisorption and f(Fwmax - v/J) is their activity in the presence of chemisorption. In Eq. (24) the electrostatic contributions of the adsorbed molecules H2O and S to their electrochemical potentials also include the electrostatic potential energy of their dipoles in the interfacial electric field, -dftdx and are average values of the normal components of these dipoles, regarded as positive when their positive end is directed towards the solution. By substituting Eq. (24) into Eq. (23), rearranging terms, and differentiating jus with respect to [Pg.315]

A change in electrical potential energy by application of bias, V, will not be translated solely into a shift in electron Fermi level, but will be divided between a shift in Fermi level Afipn and a shift in electrostatic potential energy AEg. 

Gravitational forces play a negligible role in the ways that atoms and molecules interact with one another. Forces that arise from electrical charges are more important when dealing with atoms and molecules. One of the most important forms of potential energy in chemistry is electrostatic potential energy, E, which arises from... 

Additional sources for potential barriers in ionic systems can be driven by intrinsic ionic processes. As first described by Frenkel, the formation of a net surface charge and a compensating space charge layer relates to the energy differences required to bring various ionic species to a surface [13]. Indeed, while ionic soUds are macro-scopicaUy charge-neutral, local variations in both structure and chemistry lead to internal electrostatic potentials and electric fields. Space charge layers are formed... 

The electrostatic potential energy of interaction between two particles with electric charges qi and q2 separated by a distance r, which is given by Coulomb s law ... 

In order to understand the electrical features due to cross-linkage of the ionic macromolecules, we have proposed a periodic model to estimate the electrostatic potential energy distribution in the polyelectrolyte gel [14]. In this model, the cross-linking points of the gel are considered to be periodically distributed on the chain. In addition, it is assumed that the polymer network is made by periodic stacking of two-dimensional meshes, each a distance 2r apart. In addition, a square cross section of the meshes with a side length of a, instead of a circular cross section of polymer chain with a radius of r, was used for the simulation. We set iTrr = 8a in order to keep the same surface area as well as the same surface charge density. Therefore, we have... 

The crystal field is something like a mystery and therefore it is commonly called the effective crystal field. Strictly speaking the crystal electric field acting on the open-shell electrons of a paramagnetic ion is basically due to the electrostatic field generated by the remaining ions of the crystal. Thus the 4f electrons possess an electrostatic potential energy that may be expanded in terms of spherical harmonics... 

Figure 2.10 Electrostatic potential energy Fn(( ) and Kp(( ) of charges +0.54e and -0.54 e, respectively, at the experimental distances of the H and F nuclei of HF in H20 - HF. See Figure 2.1 for definition of (j>. The curve Vh(4>) + y 4>) is the potential energy of the HF extended electric dipole as a function of (j>. (Redrawn from [16] with permission from the Canadian Journal...

The electrostatic potential (energy needed to bring a unit positive charge from infinity to a given point) and its first and second derivatives (electric field and... 

The second route [145], considered in more detail in the following, is based, instead, on the direct evaluation of the solute electrostatic potential and electric field on the cavity. The cavity Z is discretised in ttg tiles (usually called tesserae), so that the solvent charge distribution o can be represented in terms of contributions coming from each tessera. With such approximations, the total free energy of the solute in presence of the solvent can be expressed as ... 

Electrostatic Potential— the electric potential energy at a given point in space. Mapping electrostatic potential around a molecule allows us to visualize the distribution of charge. 

Electrostatic Repulsive Forces. As the distance between two approaching particles decreases, their electrical double layers begin to overlap. As a first approximation, the potential energy of the two overlapping double layers is additive, which is a repulsive term since the process increases total energy. Electrostatic repulsion can also be considered as an osmotic force, due to the compression of ions between particles and the tendency of water to flow in to counteract the increased ion concentration. 

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