Quasi-static electric and magnetic fields in the near field region of less than one wavelength


In the near field region corresponding to less than one wavelength from an antenna or scattering object, propagation is interfered with, electric and magnetic fields are decoupled and are considered quasi-static (magnetoquasistatic/electroquasistatic fields).


If we theoretically consider a point source of electromagnetism, this will generate a uniform zone of radiation of electromagnetic waves in the form of concentric spheres/circles. If we consider an antenna as a source of electromagnetism, we have to take into account its geometric shape. An antenna as a geometric object can be compared to an array of points as shown on Fig. 1 of webpage at https://www.radartutorial.eu/06.antennas/an60.en.html.


This setting would be equivalent to dipoles with a fixed phase relationship generating multipole type fields. In the area of close proximity entitled “near field” which is found at a range of one wavelength away from the antenna, the generated field components are considered to be near-spherical and to cut across each other at right angles. Further away, in the far field, the rounding becomes less pronounced and the component fields tend to become essentially planar.


The near field is divided into two zones (Figure 1):
(a) the reactive near field characterized by multipole type fields where propagation is interfered with; as a result, a quasi-static approximation holds (we do not have radiation of electromagnetic waves);
(b) the radiative near field where propagation is released from interference allowing for radiation of waves.


In the near field region, the electric and the magnetic fields are decoupled from each other and act separately; in other words they are independent, they can be measured separately and the induced field can be calculated by combining the two independent quasi-static electric and magnetic solutions of the electromagnetic field theory. Given the quasi-static approximation, we refer to electroquasistatic and magnetoquasistatic fields.


Depending on the geometry of the antenna, it is possible that either the magnetic or the electric quasistatic field is dominant. By choosing an appropriate antenna e.g. in the form of a coil, we can create a dominant magnetoquasistatic field equivalent to magnetoquasistatic waves which can find applications among others in navigation.


In the radiative near field, we observe the initial phase of coupling of the electric and magnetic field, with one regenerating the other, leading to electromagnetic wave propagation.


In the far field, the electric and the magnetic field are coupled and electromagnetic wave propagation occurs.



Figure 1: Field regions for an antenna (Wikipedia)




Electromagnetic waves with wavelength of more than one order of magnitude longer than the human body (cf. 20-meter band or 14-MHz band) are considered quasi-static for it (cf. uniform exposure)


Hypothetical mechanism of remote neural monitoring: a static magnetic field can be created at a specific location using an ELF wave etc. 


Electromagnetic radiation with a wavelength of at least one order of magnitude longer than the dimensions of the human body creates a field behaviour inside the body which corresponds to a near-zone reactive field and which is quasi-static in nature (ICNIRP 2009 e-page 62). Given that the maximal length of the human body is 2 m, the above would refer to electromagnetic waves with a wavelength of at least 20 m (cf. 20-meter band or 14-MHz band) or a frequency which is lower than 14 MHz. The electric and magnetic fields are considered to be decoupled and to act separately and additively in the tissue medium (Lin et al 1973; Lin 2000b; 2007, cited by ICNIRP 2009). The induced fields can be calculated by combining the quasi-static electric and magnetic solution of the electromagnetic field theory. In other words, the general exposure to EM fields can be determined by superpositions of the results obtained separately.




Maxwell's equations: ordinary current and displacement current


The interaction of electromagnetic fields with a specific material medium including the human body is described by Maxwell’s equations. Maxwell introduced the notion of the displacement current.


An ordinary electric current, termed conduction current, is represented by the flow of electric charges. This current, whether it is steady or time-varying, it creates a magnetic field. The conduction electric current is described by Ohm’s law.


A time-varying magnetic field creates a time-varying electric field which can be represented by an electric current which is termed displacement current. In this case, we consider that we have just a slight shift of charges from their original position as opposed to the extensive movement of flow. The displacement current notion was introduced by Maxwell. It is noted that this current does not obey Ohm’s law.


The displacement current accounts for the continuity of magnetic effects in a capacitor (ref.). In a capacitor, due to the presence of insulating material, termed dielectric, electric charges do not flow from one plate to the other via this dielectric. Current (i.e. conduction current) flows to the plates through the wires connected to the capacitor during charging and discharging. However, we consider that there exists a displacement current between the plates of the capacitor which is equal to the conduction current (ref.).


The displacement current plays a central role in the propagation of electromagnetic waves as the varying magnetic field is associated with a varying electric field which can be conceived as a displacement current.



Electromagnetic properties 


The interaction of electromagnetic fields with a specific material medium including the human body depends on its electric and magnetic properties:

  1. electrical permittivity

  2. electrical conductivity (reciprocal of electrical resistivity)

  3. magnetic permeability 


The above are abbreviated as permittivity (linked to displacement current), conductivity (linked to conduction current) and permeability.


It is noted that we often use the following relative quantities with respect to free space/vacuum:

(a) relative permittivity or relative dielectric constant (historic synonym)

(b) relative permeability



Definitions: conductor, insulator, dielectric, electric susceptibility, (relative) permittivity, dielectric constant


Conductor: A conductor is an object or material that allows the flow of electrical current. https://en.wikipedia.org/wiki/Electrical_conductor


Insulator: An electrical insulator is a material that does not allow the flow of electric current. Its internal electric charges do not flow freely under the influence of an electric field. The property that distinguishes an insulator is resistivity.



Dielectric: A dielectric is an electrical insulator which does not allow flow of electric charges but only a slight shift from their average equilibrium positions (displacement current) causing dielectric polarization. https://en.wikipedia.org/wiki/Dielectric


Conductivity: A measure of how easily a charge can pass through a material.


Electric susceptibility: The electric susceptibility "of a dielectric material is a measure of how easily it polarizes in response to an electric field. This, in turn, determines the electric permittivity of the material." https://en.wikipedia.org/wiki/Dielectric


Permittivity & relative permittivity: "Permittivity is a material property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum." https://en.wikipedia.org/wiki/Relative_permittivity


Dielectric constant is the historical term for relative permittivity.

"Permittivity ε "is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium." https://en.wikipedia.org/wiki/Permittivity


The vacuum permittivity ε0 (also called permittivity of free space or the electric constant) appears in the Coulomb force constant.




Interaction (coupling) of electric and magnetic fields with the human body


The magnetic permeability of the human body is approximately equal to that of free space. This means that the magnetic field in the human body is approximately equal to that applied externally or that the magnetic field penetrates fully the human body. It is said that the magnetic field is not disturbed by the presence of a human.


The electrical permittivity and electrical conductivity of the biological body depends on the tissue and the frequency. At low frequencies, electrical conductivity is dominant, while at high frequencies electrical permittivity tends to become dominant. It is said that the electric field is disturbed by the presence of a human.


A time-varying magnetic field induces an electric field in the body whose magnitude diminishes from the surface towards the center of the body. As a result, electric fields of circular or loop nature are created resembling a vortex or eddy, which are termed Eddy currents (or Foucault's currents). This is linked to the skin effect of conductors which finds applications among others in shielding.


However, it should be noted that this assumes that the body has homogeneous conductivity. The relevant equations should be applied to each organ or tissue of a given conductivity which behaves as a unit with its own radius.


For extremely low frequencies (ELF), the electrical permittivity and electrical conductivity of the biological body are high, but the conduction current is much greater than the displacement current. The biological body is considered as a conductive medium.


An electric field of very high voltage such as that of a transmission line (ELF) will cause current flow via electromagnetic induction to a human situated under it due to the large voltage difference.


In general, static and low frequency fields do not penetrate the human body due to its conductivity, but instead they cause movements of electric charges on the body surface as mentioned at the next section.







Static and low frequency fields generate surface charges on the human body (surface charging) via electrostatic induction


Generation of positive ions and negative ions or free electrons

Hypothetical mechanism of remote neural monitoring: possibility to use proton and electron double resonance (cf. electron clouds) 


Static or low-frequency electric field forces acting on a conductive body cause movements of electric charges on the body surface. This process is known as electrostatic induction (ref.). The surface is charged, while the interior of the conductive body could be practically field-free.




Additional references