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In the gas phase, is often defined as the diffusional mean free path, by assuming that a simple approximate relation is exact: =, where is the root mean square speed of the gas molecules: =, where is the mass of the diffusing species. This approximate equation becomes exact when used to define the diffusional mean free path.
For a classical system (e.g. Boltzmann gas), it reads: = where: k B is the Boltzmann constant; T is the absolute temperature; e is the electric charge of an electron; For a metal, described by a Fermi gas (Fermi liquid), quantum version of the Einstein relation should be used.
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
In electromagnetism, an eddy current (also called Foucault's current) is a loop of electric current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnetic field. Eddy currents flow in closed loops within conductors, in planes ...
The ampere is an SI base unit and electric current is a base quantity in the International System of Quantities (ISQ). [4]: 15 Electric current is also known as amperage and is measured using a device called an ammeter. [2]: 788 Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers.
Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. [2] [3] It is named after Friedrich Paschen who discovered it empirically in 1889. [4]
Eq.2b is a fundamental equation for most of discrete models. The equation can be solved by recurrence and iteration method for a manifold. It is clear that Eq.2a is limiting case of Eq.2b when ∆X → 0. Eq.2a is simplified to Eq.1 Bernoulli equation without the potential energy term when β=1 whilst Eq.2 is simplified to Kee's model [6] when β=0
However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material. Charge carrier densities involve equations concerning the electrical conductivity, related phenomena like the thermal conductivity, and chemicals bonds like covalent bond.