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The electric potential at infinity is assumed to be zero. In electrodynamics, when time-varying fields are present, the electric field cannot be expressed only as a scalar potential. Instead, the electric field can be expressed as both the scalar electric potential and the magnetic vector potential. [2]
Many times in the use and calculation of electric and magnetic fields, the approach used first computes an associated potential: the electric potential, , for the electric field, and the magnetic vector potential, A, for the magnetic field. The electric potential is a scalar field, while the magnetic potential is a vector field.
As the term suggests, an EM field consists of two vector fields, an electric field (,) and a magnetic field (,).Both are time-dependent vector fields that in vacuum depend on a third vector field (,) (the vector potential), as well as a scalar field (,)
The scalar potential is an example of a scalar field. Given a vector field F, the scalar potential P is defined such that: [1] = = (,,), where ∇P is the gradient of P and the second part of the equation is minus the gradient for a function of the Cartesian coordinates x, y, z. [a] In some cases, mathematicians may use a positive sign in front ...
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.
The EFIE describes a radiated field E given a set of sources J, and as such it is the fundamental equation used in antenna analysis and design. It is a very general relationship that can be used to compute the radiated field of any sort of antenna once the current distribution on it is known.
Introducing the electric potential φ (a scalar potential) and the magnetic potential A (a vector potential) defined from the E and B fields by: =, =.. The four Maxwell's equations in a vacuum with charge ρ and current J sources reduce to two equations, Gauss's law for electricity is: + =, where here is the Laplacian applied on scalar functions, and the Ampère-Maxwell law is: (+) = where ...
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 ...