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Continue reading...Main Point: The electric vector potential offers a means of determining the non-conservative component of a mixed stationary or quasi-stationary electric field

While many are familiar with the static magnetic vector potential

## \bf A = (\mu/4\pi) \int \bf j~ dv/s ##

with ## \bf j ## = current (area) density within differential volume ## dv ## and ## s ## = distance from ## dv ## to the point of observation, the magnetic field is then derivable from

## \bf B = \nabla \times \bf A ##.

However, finite vector potentials exist in any vector field ## F ## for which ## \nabla \times \bf F \neq 0 ##. If the field is wholly scalar the vector potential is zero.

The Helmholtz decomposition theorem can be reduced for any electric field to stating that there are two kinds of E field, one for which ## \nabla \times \bf E = 0 ## (a “scalar” field ## E_s ##), and the other for which ## \nabla \times \bf E \neq 0 ##, a non-conservative field ## E_m ##. An E field can comprise both kinds of...