Time-Varying Fields

This chapter begins with Faraday’s law and its applications. It discusses different cases of electromagnetic induction including that for stationary loop located in a time-varying magnetic field, time-varying closed contour in time-invariant magnetic field, time-varying closed contour in time-varying magnetic field, and the closed contour with two adjacent moving sides in time-varying magnetic field. It also discusses the nature and conceptual aspects of the displacement current. It discusses Maxwell’s equations in integral and point form and the boundary conditions for time-varying fields. It describes the modification of gradient relation and Poisson’s equation for scalar electric and vector magnetic potentials. It includes a detailed discussion on the Poynting theorem, an alternative Poynting theorem, and their comparison. This chapter also describes the relativistic effects on field relations. This includes the special theory of relativity, Maxwell’s views, and the Lorentz transformation. It discusses Maxwell’s equations for moving media, force on stationary charges due to steady conduction currents, the second observer paradox, magnetostatic field as the relativistic effect of electrostatic field, relativistic effects on time-independent fields, and energy density of line currents and surface currents.