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2.1: Definitions

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    Continuum electromechanics brings together several disciplines, and so it is useful to summarize the definitions of electrodynamic variables and their units. Rationalized MKS units are used not only in connection with electrodynamics, but also in dealing with subjects such as fluid mechanics and heat transfer, which are often treated in English units. Unless otherwise given, basic units of meters (m), kilograms (kg), seconds (sec), and Coulombs (C) can be assumed.

    Table 2.1.1 Summary of electrodynamic nomenclature
    Name Symbol Units
    Discrete Variables
    Voltage or potential difference \(v\) \([V] = volts = m^2 kg/C sec^2\)
    Charge \(q\) \([C] = Coulombs = C\)
    Current \(i\) \([A] = Amperes = C/sec\)
    Magnetic flux \(\lambda\) \([Wb] = Weber = m^2 kg/C sec\)
    Capacitance \(C\) \([F] = Farad = C^2 sec^2 /m^2 kg\)
    Inductance \(L\) \([H] = Henry = m^2 kg/C^2\)
    Force \(f\) \([N] = Newtons = kg m/sec^2\)
    Field Sources
    Free charge density \(\rho_f\) \(C/m^3\)
    Free surface charge density \(\sigma_f\) \(C/m^2\)
    Free current density \(\overrightarrow{J_f}\) \(A/m^2\)
    Free surface current density \(\overrightarrow{K_f}\) \(A/m\)
    Fields (name in quotes is often used for convenience)
    "Electric field" intensity \(\overrightarrow{E}\) \(V/m\)
    "Magnetic field" intensity \(\overrightarrow{H}\) \(A/m\)
    Electric displacement \(\overrightarrow{D}\) \(C/m^2\)
    Magnetic flux density \(\overrightarrow{B}\) \(Wb/m^2 (tesla)\)
    Polarization density \(\overrightarrow{P}\) \(C/m^2\)
    Magnetization density \(\overrightarrow{M}\) \(A/m\)
    Force density \(\overrightarrow{F}\) \(N/m^3\)
    Physical Constants
    Permittivity of free space \(\varepsilon_o = 8.854 \times 10^{-12}\) \(F/m\)
    Permeability of free space \(\mu_o = 4\pi \times 10^{-7}\) \(H/m\)

    Although terms involving moving magnetized and polarized media may not be familiar, Maxwell's equations are summarized without prelude in the next section. The physical significance of the unfamiliar terms can best be discussed in Secs. 2.8 and 2.9 after the general laws are reduced to their quasistatic forms, and this is the objective of Sec. 2.3. Except for introducing concepts concerned with the description of continua, including integral theorems, in Secs. 2.4 and 2.6, and the discussion of Fourier amplitudes in Sec. 2.15, the remainder of the chapter is a parallel development of the consequences of these quasistatic laws. That the field transformations (Sec. 2.5), integral laws (Sec. 2.7), splicing conditions (Sec. 2.10), and energy storages are derived from the fundamental quasistatic laws, illustrates the important dictum that internal consistency be maintained within the framework of the quasistatic approximation.

    The results of the sections on energy storage are used in Chapter 3 for deducing the electric and magnetic force densities on macroscopic media. The transfer relations of the last sections are an important resource throughout all of the following chapters, and give the opportunity to explore the physical significance of the quasistatic limits.


    This page titled 2.1: Definitions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James R. Melcher (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.