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The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 2).
In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, [1] equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured ...
An I–V curve which is a straight line through the origin with positive slope represents a linear or ohmic resistor, the most common type of resistance encountered in circuits. It obeys Ohm's law; the current is proportional to the applied voltage over a wide range. Its resistance, equal to the reciprocal of the slope of the line, is constant ...
where D is the diffusion coefficient for the electron in the considered medium, n is the number of electrons per unit volume (i.e. number density), q is the magnitude of charge of an electron, μ is electron mobility in the medium, and E = −dΦ/dx (Φ potential difference) is the electric field as the potential gradient of the electric potential.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The Lennard-Jones potential is a simple model that still manages to describe the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and eventually stop interacting at infinite distance, as shown in the Figure.
The atmospheric potential gradient leads to an ion flow from the positively charged atmosphere to the negatively charged earth surface. Over a flat field on a day with clear skies, the atmospheric potential gradient is approximately 120 V/m. [ 18 ]
In generic terms, electrochemical potential is the mechanical work done in bringing 1 mole of an ion from a standard state to a specified concentration and electrical potential. According to the IUPAC definition, [4] it is the partial molar Gibbs energy of the substance at the specified electric potential, where the substance is in a specified ...