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  2. Velocity potential - Wikipedia

    en.wikipedia.org/wiki/Velocity_potential

    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.

  3. Mathematical descriptions of the electromagnetic field

    en.wikipedia.org/wiki/Mathematical_descriptions...

    The potential equations can be simplified using a procedure called gauge fixing. Since the potentials are only defined up to gauge equivalence, we are free to impose additional equations on the potentials, as long as for every pair of potentials there is a gauge equivalent pair that satisfies the additional equations (i.e. if the gauge fixing ...

  4. Liénard–Wiechert potential - Wikipedia

    en.wikipedia.org/wiki/Liénard–Wiechert_potential

    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 ...

  5. Lorenz gauge condition - Wikipedia

    en.wikipedia.org/wiki/Lorenz_gauge_condition

    Note added on 26 November 2024: It should be pointed out that Lorenz actually derived the 'condition' from postulated integral expressions for the potentials (nowadays known as retarded potentials), whereas Lorentz (and before him Emil Wiechert) imposed it on the potentials to fix the gauge (see, e.g, his 1904 Encyclopedia article on electron ...

  6. Gauge theory - Wikipedia

    en.wikipedia.org/wiki/Gauge_theory

    The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge ...

  7. Gauge fixing - Wikipedia

    en.wikipedia.org/wiki/Gauge_fixing

    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 ...

  8. Retarded potential - Wikipedia

    en.wikipedia.org/wiki/Retarded_potential

    Position vectors r and r′ used in the calculation. The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: =, = where φ(r, t) is the electric potential and A(r, t) is the magnetic vector potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator. [2]

  9. Electric potential - Wikipedia

    en.wikipedia.org/wiki/Electric_potential

    In electrodynamics, the electric potential has infinitely many degrees of freedom. For any (possibly time-varying or space-varying) scalar field, 𝜓, we can perform the following gauge transformation to find a new set of potentials that produce exactly the same electric and magnetic fields: [5]