Chirality spelt capacitance
The Lorentz force has two components. The electric force acts in the direction of the electric field for positive charges and opposite to it for negative charges, tending to accelerate the particle in a straight line. The magnetic force is perpendicular to both the particle's velocity and the magnetic field, and it causes the particle to move along a curved trajectory, often circular or helical in form, depending on the directions of the fields.
Variations on the force law describe the magnetic force on a current-carrying wire (sometimes called Laplace force), and the electromotive force in a wire loop moving through a magnetic field, as described by Faraday's law of induction.[1]
Together with Maxwell's equations, which describe how electric and magnetic fields are generated by charges and currents, the Lorentz force law forms the foundation of classical electrodynamics.[2][3] While the law remains valid in special relativity, it breaks down at small scales where quantum effects become important. In particular, the intrinsic spin of particles gives rise to additional interactions with electromagnetic fields that are not accounted for by the Lorentz force.
Historians suggest that the law is implicit in a paper by James Clerk Maxwell, published in 1865.[1] Hendrik Lorentz arrived at a complete derivation in 1895,[4] identifying the contribution of the electric force a few years after Oliver Heaviside correctly identified the contribution of the magnetic force.[5]
This device consists of a conducting flywheel rotating in a magnetic field with one electrical contact near the axis and the other near the periphery. It has been used for generating very high currents at low voltages in applications such as welding, electrolysis and railgun research. In pulsed energy applications, the angular momentum of the rotor is used to accumulate energy over a long period and then release it in a short time.
In contrast to other types of generators, the output voltage never changes polarity. The charge separation results from the Lorentz force on the free charges in the disk. The motion is azimuthal and the field is axial, so the electromotive force is radial. The electrical contacts are usually made through a "brush" or slip ring, which results in large losses at the low voltages generated. Some of these losses can be reduced by using mercury or other easily liquefied metal or alloy (gallium, NaK) as the "brush", to provide essentially uninterrupted electrical contact
The lower dielectric constant in ice
3 vs 80 similar to weak glass vs H2O
implies that it takes a higher ev barrier to cause the same degree of reorientation of molecules away from existing hexagonal octagonal structure as ice aka
Deprotonation is the removal of a positively charged proton H3O+ from a molecule of H2O in a solution of H2O leaving behind a new species called a conjugate base.OH- aka
The electron.
This causes a redistribution of electron density within the molecule, making OH- "electron-rich." The electrons themselves remain localized in the molecule's orbitals.
Overall negative charge: The hydroxide ion has an overall negative charge, which is a key indicator of electron richness. In the formation of OH- an extra electron is …"gained", typically from a metal in an ionic compound like sodium hydroxide (NaOH) or through the autoionization of water.
2. Through the autoionization of water The autoionization of water is the transfer of a proton from one water molecule to another, forming a hydronium ion H3O+ and a hydroxide ion OH⁻. This is a reversible process with a very small equilibrium constant
2H2O <= => H3O+ a proton + OH- an electron
Explaining this in eV terms requires considering 1. The energy to break the O-H covalent bond and
2. the energy gained from forming the new bonds and
3. stabilizing the ions through solvation.
Bond dissociation energy: A significant amount of energy is needed to break the O-H bond in a water molecule. Breaking the first O-H bond requires about
Electron affinity of the hydroxyl radical: The resulting neutral hydroxyl radical (OH) has a strong affinity for an electron to become the hydroxide ion (OH⁻). The electron affinity for the OH radical is about
Proton affinity of water: The proton lost from one water molecule is accepted by another water molecule. The energy released when a water molecule accepts a proton is its proton affinity
The standard enthalpy change H for the autoionization of water is endothermic and approximately +55.8 kJ/mol at 25°C. Other reported values are similar, such as +56.78 kJ/mol. The endothermic nature of this reaction is confirmed by the fact that the autoionization constant of water Kw increases with increasing temperature. According to Le Châtelier's principle, if a reaction is endothermic (absorbs heat), increasing the temperature will shift the equilibrium to favor the products. This results in higher concentrations of H3O+ protons and OH- electron "ions" at higher temperatures.
Net effect and solvation: Summing the gas-phase energy changes gives a positive value, indicating that the reaction is highly unfavorable in the gas phase. However, in liquid water, the high polarity and hydrogen bonding create a stabilizing effect through solvation. .
The Special Case of H₃O⁺ and OH⁻ The hydration energies of \(H_{3}O^{+}\) and $OH^-$ are particularly difficult to calculate because these ions are not simple, static spheres.
They are central to the water autoionization equilibrium and are part of a constantly shifting network of hydrogen bonds, rapidly transferring protons through the water.
This phenomenon, known as the Grotthuss mechanism, means that the "hydronium" and "hydroxide" ions exist as larger, transient structures like \(H_{9}O_{4}^{+}\) (Eigen cation) or \(H_{5}O_{2}^{+}\) (Zundel cation).
The hydration free energies for these species are very large, on the order of 100 kcal/mol, making a high degree of accuracy necessary for reliable calculations. The currently accepted values for the standard hydration free energy (\(\Delta G_{hyd}^{\circ }\)) are: \(H_{3}O^{+}\) (proton hydration): ~-1104.5 kJ/mol$OH^-$: The value is often derived in relation to the proton, with its hydration energy estimated to be approximately -437 kJ/mol. However, there is still significant debate over the most accurate single-ion values.
Three lone pairs: The oxygen atom in hydroxide has three lone pairs of electrons and shares one pair with the hydrogen atom. This high concentration of non-bonding electrons makes the oxygen center electron-dense.
High dielectric constant of liquid water:
As liquid water, at the surface thermal containing pressure is sufficient to allow individual water molecules to rotate and reorient their permanent electric dipoles in response to an external electric field. This collective reorientation is the primary mechanism behind liquid water's high dielectric constant of ~80. The energy barrier to break hydrogen bonds and reorient is low, a fraction of an eV.
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