Generalities on the Theory of the Electromagnetic Field and on the Structure of Substance
47
permits, in many applications, to simplify the calculations and ensures a very good accuracy. The true electric charge and electric field strength in vacuo are primitive (fundamental) quantities in the framework of the microscopic theory, as well as in the framework of the macroscopic theory of the electromagnetic field. The particles with electric charge, like electrons and ions, which can move carrying electric charge, are called electric charge carriers. In many cases, it is necessary to consider small bodies with electric charge. Since the electric charge, as mentioned above, is a property of bodies, the more exact wording is one of the following: A small body charged with the electric charge q; a point-like charge q; a point charge q. The electric charge of a body is also denoted by q and can be termed electric charge or quantity of electricity. The unit (of measure) of electric charge in the SI system of units is the coulomb (symbol C); its definition will be examined in Section 1.15.
1.6.3. Density of Electric Charge The local state of electrification is characterized by the volume distribution of the electric charge. The volume density of the electric charge at any point of the body is defined as the ratio of the following quantities: The electric charge, denoted q 6 , contained within the domain bounded by a small closed surface 6 including that point, and the volume 'v bounded by the above surface, which is a physically infinitesimal volume. As a macroscopic quantity, the electric charge may be considered continuously distributed in the space occupied by any body. In this case, the macroscopic volume density of the electric charge may be introduced in the form: Uv
'q 6 'v o0 'v lim
d q6 . dv
(1.7)
The electric charges may sometimes be distributed in a very thin layer over certain surfaces. Then, the idealized macroscopic case will be considered. In this case, the electric charge is distributed on these surfaces, considered as discontinuity surfaces. Therefore, the macroscopic surface density of the electric charge may be introduced in the form: Us
lim
'S o0
'q S 'S
d qS . dS
(1.8)
The electric charges may sometimes be distributed very non-uniformly and may be concentrated about certain lines. Also, the idealized macroscopic case will be considered. In this case, the electric charge is distributed along these lines, considered as discontinuity lines. The macroscopic line density of the electric charge may be introduced in the form: Ul
'ql 'l o0 'l lim
d ql . dl
(1.9)
