ABSTRACT
This chapter discusses the law of magnetic induction which is the basis for Maxwell’s first equation. It illustrates the geometry used for the mathematical description of the magnetic induction phenomenon. The chapter introduces the concept of field operators by solving a simple problem of mechanics that consists in calculating the work performed by a force in dragging a body along a closed path. It describes the derivation of the integral form of Maxwell’s second equation, which generalized Ampère’s circuital law. Maxwell’s third equation translates the behavior of the magnetic flux density field lines. The expression of Maxwell’s third equation in a differential form uses the divergence concept of a vector field. Maxwell’s fourth equation is derived from electrostatic Gauss’s law, which establishes that the displacement vector flux over a closed surface is equal to its internal charge. The continuity equation, or conservation law of electric charges, can be deduced from Maxwell’s equations.
