The Vector and Scalar Potential via Relativity

Abstract

It is sometimes more convenient to solve problems in classical electromagnetism by introducing the scalar potential ϕ and the vector potential A. The full definitions of ϕ and A and the differential equations for ϕ and A will be developed from Maxwell’s equations in Section 5.7. For the present, it will be sufficient to assume that ϕ and A are related to the electric intensity E and the magnetic induction B by the equations

$$E = - \nabla \phi - \frac{{\partial A}}{{\partial t}}$$

(5.1)

$$B = \nabla \times A$$

(5.2)