Page 82 - Maxwell House

62 Chapter 2

∘ where − means that we decided to start now from walking along in the
− ∫ 2 2 2
− 2
direction to . Therefore, the definition of potential will be unique if and only if
1
∘ = ∮ ∘ = 0 (2.37)
∫ ∘ + ∫
1 − 2
Equation (2.37) tells us that the potential might be defined uniquely if work done in electric

st
field around a closed loop L is zero. Looking back at 1 Maxwell’s equation (1.41) we see that

∮ ∘ = − ∬ ∘ (2.38)

Consequently, the equation (2.37) is correct or almost correct while ∬ ∘ → 0.

Therefore, the resistor is a real resistor as long as its all geometrical dimensions are quite small
relative to the wavelength (≤ /10 is a decent criteria).
2.2.9 Per Square Resistance
In case of uniformly distributed static or close to static electrical field parallel to the axis Y, as
shown in Figure 2.2.11, all integrals in (2.35) can be done and

1 [Ω] (2.39)
= =
∙
Here A = w ∙ is the end-wall area. The ratio l/A in (2.39) is called a geometry factor. In the
literature one can find the term “resistance in Ohms per square.” To clarify this definition let
rewrite the equation (2.39) in the form

1
= = (2.40)
∙ □

a) b)

Figure 2.2.13 a) Antenna and b) Aircraft testing in an anechoic chamber

1
Here = is measured in Ohms and called “Ohms per square” resistance while the product
□
∙
= ∙ [S] is called surface conductivity. Note that the ratio l/w is dimensionless making

(2.40) quite convenient for measurement. The title “Ohms per square” or “surface resistance”
came from the thin film technology based on deposition of resistive films onto some flat or
conformal insulating substrate. Sheet resistance measurements are very common to characterize
the uniformity of conductive or semiconductive coatings and materials, e.g. for quality
assurance.