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The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by: [1] =, where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.
The drift velocity is the average velocity of the charge carriers in the drift current. The drift velocity, and resulting current, is characterized by the mobility; for details, see electron mobility (for solids) or electrical mobility (for a more general discussion). See drift–diffusion equation for the way that the drift current, diffusion ...
The drift velocity is therefore: = =, where is the mean free time Since we only care about how the drift velocity changes with the electric field, we lump the loose terms together to get v d = − μ e E , {\displaystyle v_{d}=-\mu _{e}E,} where μ e = e τ c m e ∗ {\displaystyle \mu _{e}={\frac {e\tau _{c}}{m_{e}^{*}}}}
The grad-B drift can be considered to result from the force on a magnetic dipole in a field gradient. The curvature, inertia, and polarisation drifts result from treating the acceleration of the particle as fictitious forces. The diamagnetic drift can be derived from the force due to a pressure gradient.
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The relativistic velocity is given by the (time-like) changes in a time-position vector = ˙, where =, (which shows our choice for the metric) and the velocity is = / (). The proper (invariant is an inadequate term because no transformation has been defined) form of the Lorentz force law is simply
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [1] The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point.
A solution to the one-dimensional Fokker–Planck equation, with both the drift and the diffusion term. In this case the initial condition is a Dirac delta function centered away from zero velocity. Over time the distribution widens due to random impulses.