Some Properties of Time-Dependent Fields

The effort required to calculate time-dependent systems is significantly larger than for calculating static systems. So, everything has to be done to keep the complexity within tolerable limits. First, a decoupled scalar differential equations system will be introduced. These equations deal with potentials. The decoupling of space and time components is done using a method known as gauging. The equations obtained in this way determine the behaviour of electromagnetic waves in space and at material boundaries. As a result, the laws of optics emerge. It is also shown that time-dependent fields always carry energy and momentum—sometimes in a counter-intuitive way. Limits for simplifications by using quasi-static approximations are discussed. The chapter ends with a description of the electrical behaviour of cables.