It has been known for about a hundred years that electric and magnetic fields that satisfy Maxwell's equations can sometimes be derived from two scalar functions. Scalar potentials have been investigated many times in the hope that analyses that are made in terms of the six interrelated components of the electric and magnetic fields could be simplified by describing fields in terms of two quantities that are relatively simple to compute. This paper reviews investigations of scalar potentials that have been made over the years. It discusses possible definitions of scalar potentials and describes their properties. This includes a requirement that scalar potentials be defined in terms of a preferred direction. The functional form of components of the electric and magnetic fields in the preferred direction, in terms of the scalar potentials, is different from the forms of the field components in the other two directions. It describes applications to boundary value problems and to the computation of electric and magnetic fields generally. Restrictions on coordinate systems hi which scalar potentials can be used are discussed. These restrictions, combined with the requirement of a preferred direction, limit the use of scalar potentials to specific geometries. The relationships of scalar potentials to charge and current sources of electromagnetic fields are described. It is shown that scalar potentials cannot always be used in regions where charges or currents are present. The limitations that these restrictions impose are discussed. Some computational examples on the use of electromagnetic scalar potentials are given. It is demonstrated that, when it is possible to describe a problem in terms of scalar potentials, their use can lead to a considerable simplification of the calculations.
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