4.2 Magnetic Media, Inductance, Energy, Ohm's Law and the Joule Phenomenon

Section 4.1 built magnetostatics in empty space: the Lorentz force, the Biot–Savart law, the vector potential and the two fundamental equations, $\nabla \times H=J$ and $\nabla \cdot B=0$, with Ampère's law as the working tool. In this section we let matter in, in exactly the way Section 3.4 did for electrostatics. An iron core multiplies the field of a coil a thousandfold, a steel sheet bends magnetic field lines almost into its surface, and a magnet keeps a field without any battery. All of this comes from the same idea as before: the material answers the applied field with sources of its own, which here are tiny circulating currents.

The plan follows the lecture. We first describe the magnetic medium (magnetisation, bound currents, $H$, susceptibility and ${\mu }_r$), state the fundamental equations in a medium and derive the boundary conditions at an interface. Then we turn to circuits: the force between two current loops leads to the mutual and the self inductance, to the magnetic energy, and to the two laws of conduction, Ohm's law and the Joule phenomenon. Finally the current loop is shown to be a magnetic dipole and its torque is found. Three applications are placed right after the theory they use: ferromagnetic materials, the transformer and the loudspeaker.