Electrodynamics in formulae

International Journal of Electrical Engineering Education, Jul 1997 by Potolea, E

Abstract I have revised the general theory of physical quantities and I have demonstrated that the system of primary quantities of electrodynamics is as unique as the system of the general laws of physics. I have identified three principles of electrodynamics with which help I have generalized the laws on the assumption of mobile conductors. I have demonstrated that Maxwell's and Lorentz's postulates are theorems of electrodynamics.

1 INTRODUCTION

Macroscopic, classical, non-relativistic electrodynamics, considering the hypothesis of fixed bodies, is known as `Maxwell's electrodynamics'". More than one hundred years have elapsed since the theory was experimentally confirmed and the complete, but independent set of general laws is still unknown. Maxwell's equations are sometimes completed with `the law of electric charge conservation' and a set of laws, which are not independent, is set up. The interpretation of some macroscopic phenomena with the help of the microscopic theory (dipole charges and Amperian currents) and the extension of the theory under the hypothesis of mobile bodies (Hertz) has brought no additional light to the general laws of electrodynamics.

The paper demonstrates that the singular set of general laws of electrodynamics is composed out of the electromagnetic field in vacuum. All electrodynamic laws (general laws or matter laws) can be analytically generalized using the principles of conservation of electric charge, electromagnetic energy and electromagnetic impulse.

2 ELECTRODYNAMIC PHYSICAL QUANTITIES

2.1 Elements of physical quantities theory

Physical quantities are experimentally detected or analytically defined in the process of building a physical theory: macroscopic or microscopic, classical or quantum, relativistic or non-relativistic. Detecting a physical quantity is equivalent to determining its quality (physical dimension) and quantity (measure of its magnitude). This calls for a pair of associated equivalence and order equations. Using the equivalence equation, the equivalence class A of similar physical dimension variables is selected, and a standard unit U^sub A^ epsilon A is adopted. Using the order equation a measuring procedure A = aU^sub A^ is established and the mathematical quantity a is determined, to define the 'measure' or `numerical value' of the physical quantity A Epsilon A.

Length and time are detected using the pairs of associated equation pair (for equivalence and order) which is a result of axioms in Euclidean geometry and set theory. The other physical quantities are detected using due pairs of associated equations obtained from equality equations, physical laws and theorems.

When detecting physical quantities, two sets of macroscopic laws are selected: general laws and material laws. Physical quantities which are necessary and sufficient to state the general laws are called primary quantities, while the other ones will be called derived quantities. Two categories of primary physical quantities could be identified: universal and specific quantities. The main universal physical quantities, the length s, the time t, the force F, are indispensable when stating the general laws of mechanics, thermodynamics and electrodynamics. The specific primary quantities can be state quantities or universal physical constants.

The physical quantities, for which independent units of measure are chosen, are called fundamental quantities of the system of units of measure, while the others are called secondary quantities. The number of the fundamental quantities (NF) is obtained from NF = NP - NG, where NP is the number of primary quantities and NG is the number of general laws. The first fundamental quantities are the universal ones, that is length, time and force. The independent units of measure internationally agreed by SI are the meter (m) for length, the second (s) for time and the kilogram (kg) for mass. Force is considered as a derived quantity for which a coherent unit of measure is chosen: the Newton (N). 2.2 The electrodynamic primary quantities (Table 1)

The primary quantities of electrodynamics are the universal ones (length, time and force), the specific primary quantities (two global state quantities, q and i), four local state quantities E, D, FI, B and two physical constants Eo and po. Two test bodies are prepared: point conductors in the electricity state q and to linear conductors in the electro-kinetical state i. Equations (1) and (2) can be experimentally proven and it comes out that Eo and po are universal physical constants. The unit of measure Ampere (A) for the electric current is chosen and the following are consecutively determined: the numerical value of the go constant from equation (2), the numerical value of the so constant from equation (3) and the unit of measure for q from the first equation (31). The local state quantities for the electromagnetic field are experimentally determined, using equations (5) and (6), and analytically computed using equations (7) and (8).