Electricity and Magnetism

Charge is conserved, quantised, and comes in two signs, and the force between two of it falls off as the inverse square of the distance, measured on a torsion balance in 1785.

Divide the force by the charge that feels it and what is left belongs to the space itself: the field of a point charge, superposition turned into an integral, and the dipole that falls off faster than either charge in it.

Count the field crossing a closed surface and the answer depends only on the charge inside it, which is Coulomb's inverse square restated in a form that solves a sphere in three lines.

The electric force is conservative, so the work per unit charge is a function of position alone, and one scalar function carries everything the vector field knows.

How much charge a pair of conductors holds per volt, what it costs to put it there, and why the energy is best thought of as living in the field rather than on the plates.

Charge in steady motion, the astonishingly slow drift that carries it, why Ohm's law is a property of materials rather than a law, and the two rules that solve any network.

A force that depends on velocity and acts sideways needs a field defined by its effect rather than by a force per unit charge, and everything from the mass spectrometer to the electric motor follows from the definition.

What makes a magnetic field: the contribution of a current element, the field of a wire and a solenoid, the force that once defined the ampere, and the missing law that has no charges in it.

A magnetic field produces no current, and a changing one produces a large one, which is the discovery that made electrical power possible and killed the electric potential.

A circuit induces on itself, which gives it something very like inertia, an energy stored in its own field, and a natural frequency built out of the two constants of electromagnetism.

Ampère's law gives two different answers for a charging capacitor, and repairing it adds one term that completes the set of four and makes light possible.

Two of the four equations, applied to a thin rectangle in empty space, give a wave equation whose speed is built from {{\epsilon }}_{{0}} and {{\mu }}_{{0}} and turns out to be the measured speed of light.