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The striking difference between the two kinds of fields is that we cannot associate electric potential with points in such an electric field and that the work done by the electric force in such a field is not zero over a closed loop.
where φ(r, t) is the electric potential and A(r, t) is the magnetic potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator.
The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula.
A Langmuir probe is a device named after Nobel Prize winning physicist Irving Langmuir, used to determine the electron temperature, electron density, and electric potential of a plasma.