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If ϕ is a velocity potential, then ϕ + f(t) is also a velocity potential for u, where f(t) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable. The Laplacian of a velocity potential is equal to the divergence of the corresponding flow.
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations , these describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in ...
A particular choice of the scalar and vector potentials is a gauge (more precisely, gauge potential) and a scalar function ψ used to change the gauge is called a gauge function. [citation needed] The existence of arbitrary numbers of gauge functions ψ(r, t) corresponds to the U(1) gauge freedom of this theory. Gauge fixing can be done in many ...
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).
Consider a generic (possibly non-Abelian) gauge transformation acting on a component field = =.The main examples in field theory have a compact gauge group and we write the symmetry operator as () = where () is an element of the Lie algebra associated with the Lie group of symmetry transformations, and can be expressed in terms of the hermitian generators of the Lie algebra (i.e. up to a ...
In electromagnetism, the Lorenz condition is generally used in calculations of time-dependent electromagnetic fields through retarded potentials. [2] The condition is , =, where is the four-potential, the comma denotes a partial differentiation and the repeated index indicates that the Einstein summation convention is being used.
Electrophysiology (from Greek ἥλεκτ, ēlektron, "amber" [see the etymology of "electron"]; φύσις, physis, "nature, origin"; and -λογία, -logia) is the branch of physiology that studies the electrical properties of biological cells and tissues.
In excitable cells, the other possible states are graded membrane potentials (of variable amplitude), and action potentials, which are large, all-or-nothing rises in membrane potential that usually follow a fixed time course. Excitable cells include neurons, muscle cells, and some secretory cells in glands. Even in other types of cells, however ...