Page 40 - Maxwell House

20 Chapter 1

electric force Δ pushing or pulling this motionless ( = 0) at the starting moment of time

sensor is equal to

Δ = Δ = Δ (1.17)

where the vector of electric field strength manifests itself only by the forces exerted upon the
sensor. In other words, we can define fields as the way in which forces are spread across
distances. In accordance with Newton’s third law (for every action there is an equal and
opposite reaction) this action-at-a-distance is reciprocal. The sensor influences on the
distribution of electrical field sources by pushing and pulling them too. To avoid this impact
and to be more precise we can redefine the vector in (1.17) as a limit in macroscopic sense

−2 −1
= lim ∆ Δ = [(kg ∙ m ∙ s )/(A ∙ s) = V ∙ m ] (1.18)
⁄

Δ →0
The symbol Δ → 0 means that both the charge and object carrying the charge is lessened

together, at the same rate. Let allow the monopole sensor to move freely under electric force
influence assuming that the sensor speed is low enough and thereby the additional force
exerted by magnetic field in (1.11) is negligible. The laws of mechanics [11] tell us that the
energy required for this movement from some starting point 1 to end point 2 along the contour
L shown in Figure 1.6.1 is equal to
= ∫ ∘ [(kg ∙ m ∙ s ) ∙ m = [J = W ∙ s] (1.19)
2
−2

1
Accordingly, the energy conservation law dictates that all this kinetic energy of movement must
be delivered by the electric field . Therefore,
Δ = Δ ∫ ∘ (1.20)
2

1
Since the energy Δ is the measurable quantity, the expression (1.20) provides the mean for

the electric field strength valuation.
1.6.2 Electric Potential
In order to undo the dependence of measured energy from the sensor charge value Δ let

introduce using (1.20) the energy normalized to the test charge quantity defining the electric

potential in volts
Δ 2
= = ∫ ∘ [V] (1.21)

Δ 1
that equal the amount of work done by shifting a unit positive point-like charge down the path.
It turns out that the line integral in (1.21) and thus the potential depends on the position of two
different points, starting and ending. Therefore, electric potential measurement is always
relative and shows the difference in potential between two distinct points in the same or
different regions. One way to fix this problem of uncertainty is to shift the end point to infinity
where any meaning potential must vanish and define the absolute potential. Theoretically, it is
quite acceptable but certainly not practical. So electrical engineers decided to set our Earth’s
potential as the equivalent reference available to anyone at any time and any location.
Nevertheless, there is some additional uncertainty in (1.21). How to choose the path L? In free