To this point in our discussions, we have dealt solely with static fields. We started with static electric fields, in which all charges are stationary. The electric fields produced by these charges are stationary as well. With electric fields, we developed the notion of the electric potential, the energy stored by electric fields, and the capacitance of a configuration of conductors. We then moved on to introduce static magnetic fields, which are produced by stationary currents. For magnetic fields, we have also introduced potential functions, one a vector function, the other a scalar, but we have not yet discussed the energy stored by a magnetic field, or the inductance of a configuration of current-carrying wires. We will, of course, treat these important topics, but before we do so, we find it useful to take a first look at some time-varying effects. In particular, we will develop a law known as Faraday’s Law, which is the basis for circuit elements such as inductors and transformers, as well as electrical generators and many other useful devices. After we have mastered Faraday’s Law, we will be in a much better position to discuss the energy stored in magnetic fields and inductances, and so we will return to these topics at that time.

In the context of space weather effects, magnetosphere-ionosphere coupling is one of the fundamental processes controlling energy transfer and dissipation in geospace. Alfvén waves appear to play a key role in this coupling, specifically in coupling the dynamics of magnetospheric convection to the ionosphere and in generating the region 1 and region 2 global field-aligned current systems. The momentum transport from the magnetosphere to the ionosphere can be described as the result of the generation and propagation of Alfvén waves, for example as arising along newly reconnected magnetic field-lines, and in general in terms of their incidence on and reflection from the ionosphere. The thermosphere experiences dramatic changes in density and composition during magnetic storms. Intense Joule heating and particle precipitation at auroral latitudes cause intense thermal expansion, air upwelling and strong wind circulations. The Joule heating at E-layer altitudes can cause both density enhancements and depletions at higher altitudes, and complicate the interpretation of mass density anomalies at high latitudes. The thermospheric response to storms at middle and low latitudes is less complicated, where the averaged density enhancement is linearly proportional to the solar wind input. Magnetic substorms during active periods also cause mass density perturbations. Magnetic storms and substorms can cause disturbances up to thousands of nT at the Earth’s surface. The time derivative of the magnetic field provides a proxy for the associated geoelectric field, which can drive geomagnetically induced currents in Earthed conductors. The geoelectric field is thus a key quantity for space weather effects on technological systems such as power grids, and it can be obtained by modelling the magnetic field using ionospheric currents and model ground conductivity as inputs.