3.1.1 Fundamental assumptions

Every physical theory starts from statements that are not proved but accepted because experiment supports them. In this course we take that seriously and keep the list of such statements as short as possible. Everything else (the fields of charged lines and disks, Gauss's law, the potential, capacitance, later the laws of magnetostatics) will be derived from these few assumptions, step by step, with nothing hidden. Table 3.1.1 lists the basic assumptions of classical physics as we shall use them, together with the notions and results each one brings with it.

Table 3.1.1. The basic assumptions of classical physics and the notions they introduce. The assumptions printed in bold are the ones that electromagnetics adds to Newtonian mechanics. This section rests on assumptions 5 and 6.

	Basic assumption	Related notions and results
1	Principle of inertia (Newton)	Galilean (inertial) reference systems
2	Principle of universal attraction (Newton)	mass at rest, force
3	Universal attraction law (Newton)	attraction (gravitational) field
4	Law of motion	mass in motion
5	Principle of electrical interaction	electric charge
6	Electrical attraction law (Coulomb)	electric field
7	Lorentz force	magnetic induction
8	Biot–Savart's law	current density, magnetic field
9	Maxwell's equations	displacement current, Faraday's induction
10	Maxwell's equations in the sense of distributions	surface charges and surface currents
11	Principles of special relativity (Einstein)	4D space-time, Lorentz transformations

The first four lines are the familiar foundations of mechanics.

• The principle of inertia singles out the reference systems in which a body free of forces moves uniformly on a straight line (the Galilean, or inertial, systems). All our laws are stated in such a system.
• The principle of universal attraction says that material bodies act on one another. It introduces the notions of mass and of force.
• Newton's universal attraction law gives that force in numbers, $G{m}_1{m}_2/R^2$, and with it the idea of a gravitational field filling the space around a mass.
• The law of motion, $F=mdv/dt$, connects force with the motion of a mass.

Electromagnetics adds the lines printed in bold. The principle of electrical interaction is the experimental fact that bodies can act on each other through a property other than their mass. We call that property electric charge. Coulomb's law gives this interaction in numbers for charges at rest and leads to the notion of the electric field. These two lines are all that the present section needs.