This finds use in multipole expansions of the vector potential in electromagnetism, or the metric perturbation in the description of gravitational waves.
32.
Another expression for the vector potential, in terms of the time-retarded electric current density, has been obtained to be:
33.
These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent.
34.
In the process he introduced the magnetic vector potential, which was later shown to be equivalent to the underlying mechanism proposed by Faraday.
35.
While the velocity is the variable of interest, the existence of the stream function or vector potential is necessary by the Helmholtz Theorem.
36.
In vector calculus, a "'vector potential "'is a vector field whose curl is a given vector field.
37.
For a charged particle in an electromagnetic field, described by the scalar potential and vector potential, the momentum operator must be replaced by:
38.
The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.
39.
On introducing the external electromagnetic 4-vector potential into the Dirac equation in a similar way, known as minimal coupling, it takes the form:
40.
However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the Dirac delta function at the origin.
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