3.4.6 Permittivity & Permeability
Mr. Heaviside’s “Not So Helpful Terms”
“Some other terms put forward by Mr. Heaviside do not seem to be so helpful,” complained Irish mathematician and experimental physicist, George Minchin (1845–1914), in a review of Heaviside’s 1892 book Electromagnetic Theory:
For example the ratio of electric displacement [D] to electric force [E] at any point of a dielectric he proposes to call the “permittivity” of the medium [ε], because it indicates “the capacity for permitting electric displacement.” But a capacity for permitting is no more identified with electric displacement than with magnetic; and hence there is nothing definitely suggestive in the word [[i]].
Minchin preferred Maxwell’s own term, “coefficient of electric elasticity.” Maxwell argued that along Faraday’s “lines of force,” or field lines, there exists a kind of tension. At right angles to the field line, there is a kind of pressure. The electric field (E) exerts a force that causes a displacement (D) of equal and opposite charge, polarizing the medium. Terminology was in flux, so to speak. Maxwell also referred to the same constant as the “dielectric capacity” of a material [[ii]], and used the symbol “K.” By Heaviside’s time, practitioners preferred the Greek lower case letter, epsilon “ε,” and Heaviside’s terminology, calling this parameter the “permittivity” became standard.
The permittivity is a material property describing the ratio of electric field (E) to displacement (D), D = ε E. It shows up in the constant of Coulomb’s electric force law, and relates charge to physical force. Permittivity also shows up in Kelvin’s formula relating the intensity of the electric field to the amount of energy it holds. Figure 3.29 shows a cross section of a parallel plate capacitor, based on a figure by Maxwell [[iii]]. The figure shows the displacement field (D) which is concentrated on the left side where the dielectric material is present and more sparse on the right side where only free space separates the plates. Note also how electric field and displacement lines are always perpendicular to the conducting plates.
Permittivity bridges the gap between electrical physics and mechanical physics, quantifying the force and energy associated with electrical effects. Permeability does the same for magnetic effects. These are the physical constants that define the strength of the interaction between electromagnetic behavior and mechanical effects.
Maxwell identified the “magnetic inductive capacity” in his treatise [[iv]]. Kelvin dubbed it the “permeability” of the medium in 1872 [[v]]. In Maxwell’s thinking, magnetic fields (H) induce a phenomenon called magnetic induction or flux (B). The permeability is a material property describing the ratio of magnetic field (H) to magnetic flux (B), B = μ H. It shows up in the magnetic force law, and relates currents to physical magnetic forces. Permeability also shows up in Kelvin’s formula relating the intensity of the magnetic field to the amount of energy it holds.
Figure 3.30 shows the magnetic flux (B) field lines around a small loopstick antenna. The left side shows how the lines are more tightly confined to a high-permeability ferrite rod. The right side shows the same flux lines for the coil with the same current, but without the ferrite. The free Finite Element Method Magnetics” (FEMM) code calculates the field lines in each case [[vi]].
The fascinating aspect comes when these two parameters work together. For free space, we use a subscript “o” to denote the free-space permittivity (εo = 8.854×10-12 C2/Nm2), where “C” is Coulombs – the unit of charge, “N” is Newtons – the unit of force, and “m” is meters – the unit of distance. The free space permeability (μo = 4π×10−7 Ns2/C2) where “s” is seconds – the unit of time. The product of these electromagnetic parameters has units of inverse velocity (v) squared, and as Maxwell first noted as early as 1861, v = 1/(√εoμo) = c where c = 299,792,458 m/s is the speed of light in meters (m) per second (s). Kirchhoff’s measurement and Maxwell’s theory both suggested that light was an electromagnetic wave.
Next time: 3.4.7 What is “Free Space?”: An Æther By Any Other Name…
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References
[i] Minchin, George M., “Notices respecting New Books. Electromagnetic Theory by Oliver Heaviside,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. XXXVIII – Fifth Series, July 1894.
[ii] Treatise 1st ed. vol. 2 p. 232
[iii] After a plate by Maxwell – Fig. XII, Art 202; Treatise vol. 1.
[iv] Treatise 1st ed. vol. 2 p. 70
[v] Thomson, Theory of Induced Magnetism, 1872, p. 484.
So, what you're saying is, every capacitor is a flux capacitor? :)