Page 33 - Maxwell House

BASIC EQUATIONS OF MACROSCOPIC ELECTRODYNAMICS 13

First of all, note that EM fields can only control the behavior of objects that carry the electric
charges. Moreover, as we discussed above, any field measurement is based on the extracting
some portion of EM energy from the measured fields. Therefore, the measured fields should
slightly differ from the original ones. Also note that in reality any charged object, at rest or
moving, would generate its own EM fields, which would alter the electromagnetic force that it
experiences. Moreover, the net force must include gravity and any other forces aside from the
electromagnetic force. To minimize all such kind of effects, we assume that the hypothetical
sensor has infinitesimally small mass and charge.

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Field sensor #1 can be realized as a motionless positively charged monopole of infinitesimal
physical sizes. We denoted such point-like sensor by symbol ∆ where ∆ is the monopole

charge value. Note that almost ideal natural sensor of this type is a free electron of mass =

−31
9.10938291x10 kg carrying the negative charge =
−1.60217657x10 −19 Coulombs.
d Field sensor #2 is an electric dipole (ball-and-stick model)
defined as an assembly of two monopoles ±∆ shifted in space

Figure 1.4.1 Electric at short distance d from each other, as shown in Figure 1.4.1.
dipole. Note that the vector d points out in the direction of positive
charge. We assume that this monopole duo under the influence
of EM fields can spin as a solid assembly around their center
(blue arrows). Eventually, such element is vectorial in nature and characterized by its dipole
polarization electric moment
= ∆ [C ∙ m] (1.1)

Almost any atom and molecule in solid, liquid or gas material can behave and serve as the
natural sensor of this kind. If so, its introduction greatly simplifies
the study of EM field inside such materials as dielectrics and
semiconductors.

Field sensor #3 is the electric monopole ∆ contained inside

some small domain ∆ and moving there with speed , as shown
in Figure 1.4.2.

1.4.2 Electric Current and its Volume Density Figure 1.4.2 Positive
charge moving with
As we know, the stream of freely moving electric charges is called speed
an electric current and defined as the variation ∆ in charge

per variation ∆ in time at the given point
⁄
⁄
= − lim ∆ ∆ = − [C ∙ s −1 ] (1.2)

∆→0
Therefore, the sensor #3 can be called a current sensor. The scalar definition (1.2) came into
electrodynamics from the lumped circuit theory giving us the information about the current
magnitude only and telling nothing about the direction of charge stream. In the circuit theory,
such information is irrelevant because the direction of current and wire carrying it always
coincides.

4 common agreement