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Energy Flow in Reactive Fields

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Hans Schantz

on 19 September 2016

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Transcript of Energy Flow in Reactive Fields

What is Radiation?
Do accelerating charges radiate fields or energy?

Yes... and no, respectively.
Opens and Shorts
Superposition of Waves
Standing Waves

Key Concept:
Fields and Energy Behave Differently

Energy Flow in Reactive Fields
Hans G. Schantz

James Clerk Maxwell Foundation
18 India Street
Edinburgh EH3 6EZ
5, 6 September, 2016
Conventional Wisdom
What is the Near Field?
What is Radiation?

Electromagnetic Basics
Gauss' Law
Right-Hand Rules
Jefimenko Form
Energy Velocity

How Does Radiation Work?
Accelerating Charges
Dipole Radiation
What is the Near Field?
A charge accelerates due to an applied field.
The "kinked field line" picture is incomplete...
Radiation as "Kinked" Fields
Original Field Line
Radiation = Transverse Field Line
Change Propagates at
Speed of Light
Radiation is a transverse component in a changing field line - a "kink."
Is this a complete picture?
A charge does not accelerate of its own volition.
What is Radiation?
Radiation as a transverse kink or bend in a field line.
Heaviside (1893) presented this model.
Another early proponent was J.J. Thompson (1904)
Right-Hand Rule for Radiation
Time-Dependent Biot-Savart Law:
Hans Schantz, "Electromagnetic Radiation Made Simple," APS/AAPT Joint Meeting. Washington, D.C., April 18-21, 1997.
Royal Institution
March 12, 1832

Certain of the results of the investigations which are embodied in the two papers entitled ‘Experimental Researches in Electricity’ lately read to the Royal Society, and the views arising therefrom, in connexion with other views and experiments lead me to believe that magnetic action is progressive, and requires time, i.e. that when a magnet acts upon a distant magnet or piece of iron, the influencing cause (which I may for the moment call magnetism) proceeds gradually from the magnetic bodies, and requires time for its transmission, which will probably be found to be very sensible.

I think also, that I see reason for supposing that electric induction (of tension) is also performed in a similar progressive way.

I am inclined to compare the diffusion of magnetic forces from a magnetic pole to the vibrations upon the surface of disturbed water, or those of air in the phenomenon of sound; i.e. I am inclined to think the vibratory theory will apply to these phenomena as it does to sound, and most probably to light.

By analogy, I think it may possibly apply to the phenomenon of induction of electricity of tension also.

These views I wish to work out experimentally; but as much of my time is engaged in the duties of my office, and as the experiments will therefore be prolonged, and may in their course be subject to the observation of others, I wish, by depositing this paper in the care of the Royal Society, to take possession as it were of a certain date; and so have right, if they are confirmed by experiment, to claim credit for the views at that date; at which time as far as I know, no one is conscious of or can claim them but myself.

M. Faraday
Predicted radiation in secret 1832 letter
Letter not opened and read until 1937
"Magnetic action is progressive and requires time...
"I am inclined to compare the diffusion of magnetic forces from a magnetic pole to the vibrations upon the surface of disturbed water..."
H. Hertz,
Electric Waves
, (London: Macmillan and Co., 1893), p. 144.
The usual “radiation field” approximation…

…violates Gauss’s Law
Gauss's Law for Radiation
Are there sinks or sources associated with radiation?
What About Radiation?
Suppose we add another term…

…then Gauss’s Law (source free region) is satisfied:
Gauss' Law for Radiation
A simple calculation in the co-moving (i.e. v = 0) reference frame.
The fields are (for the charge):

(for the applied field):

From the equation of motion:

The tangential field is:

…which goes to zero for:
Exponentially Decaying Dipole
H. Hertz,
Electric Waves
, (London: Macmillan and Co., 1893), p. 152. See
Gauss' Law
In 1835, Gauss found that the electric flux through any closed surface is proportional to the enclosed electric charge.
Corollary - electric field lines begin and end on charges

Magnetic field lines are "divergenceless," i.e. a closed loop with no beginning and no end.
A radial component is needed to close the loop:

Bound field lines have:
Source (positive charge)
Sink (negative charge)
Unbound or radiation field lines are closed field lines (neither source nor sink).
For an electron, re = 2.8E-15 m is the “classical electron radius”
For an exponentially decaying dipole,

Inside: energy flows in
to be dissipated in decay.
Outside: energy radiates
Radiation energy comes
from energy stored in the
static fields - not from the region around the accelerating charges themselves.
E-Field Phase
H-Field Phase
Phase Delta
H. Schantz, "The flow of electromagnetic energy in the decay of an electric dipole," American Journal of Physics 63(6), June 1995 
Heaviside, Oliver,
Electromagnetic Theory
, Vol. 1, London: “The Electrician” Printing and Publishing Company, Limited, 1893, p. 55.
Thompson, J. J.,
Energy and Matter
, New York: Charles Scribner and Sons, 1904, p. 56.
Electromagnetic Basics
Energy velocity in terms of the normalized impedance…

Energy Velocity & Impedance
Normalized Impedance
Field Impedance
Extend application of impedance from circuits to fields,
Regard impedance as an attribute of the field as well as the medium
Sergei Schelkunoff
Oliver Heaviside
John Henry Poynting
Schelkunoff, S. A., “The Impedance Concept and Its Application to Problems of Reflection, Refraction, Shielding and Power Absorption,” The Bell System Technical Journal, Vol. 17, No. 1, 1938, p. 17-48.
Why use the more complicated Poynting-Heaviside Theory?
Skin Effect
AC Resistance
Electron Drift Velocity
Compare These Models...
Field Impedance
(courtesy Mt. Holyoke College)
Heaviside, Oliver,
Electrical Papers
, Vol. 1, London: The Electrician Publishing Company, 1892, pp. 449-450. Originally published as “Electromagnetic Induction and Its Propagation,” in The Electrician, February 21, 1885.
Poynting, John Henry, “On the Transfer of Energy in the Electromagnetic Field,” Philosophical Transactions, Royal Society, London, Vol. 175 Part II, 1885, pp. 334-361.
Electromagnetic Energy Flow
Energy Velocity
Oliver Heaviside,
Electromagnetic Theory
, Vol. 1, (London: “The Electrician” Printing and Publishing Company, 1893), pp. 78-80. See:
Harry Bateman,
The Mathematical Analysis of Electrical and Optical Wave-Motion On the Basis of Maxwell’s Equations
, Cambridge University Press, 1915, p. 6. See:
H. Schantz, “Electromagnetic Energy Around Hertzian Dipoles,” IEEE Antennas and Propagation Magazine, Vol. 43, April 2001, pp. 50-62. See:
Gerald Kaiser  “Electromagnetic inertia, reactive energy and energy flow velocity,” 2011 J. Phys. A: Math. Theor. 44 345206
Energy velocity

Oliver Heaviside (1850-1925)
Harry Bateman (1882-1946) in 1915,
< 1
Gerald Kaiser in 2011,
as a local time dependent characteristic of electromagnetic fields
The Art and Science of UWB Antennas
, 2015, p. 289-292
The Art and Science of UWB Antennas
, 2015, pp. 282-283
Oliver Lodge
Lodge, Oliver, "Electrical Theory. Letters to Dr. Lodge," The Electrician 21, 1888, p. 829-831
The Art and Science of UWB Antennas
, 2015, p. 289-292
E /H = Zs

v = c
0 <
< 1 or
1 <
< infinity
v = S/u


Normalized Lagrangian:
Reactive Fields
Assuming 1-D T-Line or

One Dimensional Transmission Line
1-D Transmission Line
Assign direction to impedance, and
Generalize the 1-D transmission line concept to higher dimensional problems in which some of the dimensions may be neglected.
Summary of the Basics
E = 0 or H = 0
= 0 or infinity
v = 0
EM Energy Flow:
Normalized Impedance:

Normalized Lagrangian:

1-D Transmission Lines
EM Velocity:
Gauss' Law
Radiation is Divergenceless
Jefimenko & Right-Hand-Rules
Jefimenko Form
Time-Dependent Biot-Savart Law:
Griffiths, David J. and Mark A. Heald, “Time-dependent generalizations of the Biot-Savart and Coulomb laws,” American Journal of Physics Vol. 59, 1991, pp. 111 117.

Jefimenko, Oleg D.,
Electricity and Magnetism
, New York: Appleton-Century-Crofts, 1966, §15-7, pp. 515 518.

Panofsky, Wolfgang K.H., and Melba Phillips,
Classical Electricity and Magnetism,
2nd ed., New York: Dover, 2005.
Time-Dependent Coulomb's Law:
Gauss' Law
Jefimenko Form
Right-Hand Rules
Energy Velocity

Gauss' Law for Radiation
The Art and Science of UWB Antennas
2015, pp. 251-257
Causal Surface Around Accelerating Charge
H. Schantz, "On the Localization of Electromagnetic Energy," Ultrawideband-Short Pulse Electromagnetics 5, 2002, pp. 89-96.
Since Sr = 0 at classical electron radius, no energy passes through this sphere around the charge

Interesting implications:
No energy can pass through this surface
EM analog to an event horizon
The Art and Science of UWB Antennas
2015, pp. 275-276
How Does Radiation Work?
Accelerating charges
Dipole Radiation

Key concept:
Fields and energy behave differently!

Radiation Isn't "Kinky"
No runaway acceleration
No "naked singularities"
Fields and energy behave differently
Accelerating Charges...
Dipole Fields & Phase
Schantz, Hans G., “On the Superposition and Elastic Recoil of Electromagnetic Waves,” FERMAT, Vol. 4, No. 2, July-August 2014 [ART-2014-Vol4-Jul_Aug-002]. See also
Gaussian Impulses
Average Energy Velocity for Various VSWR
Elemental Waves
Image Theory
Arbitrary Impulses
Schantz, Hans G., “On the Superposition and Elastic Recoil of Electromagnetic Waves,” FERMAT, Vol. 4, No. 2, July-August 2014 [ART-2014-Vol4-Jul_Aug-002]. See also
Symmetric Impulses
Spacetime Diagrams
Electromagnetic Newton's Cradle
Don't Cross the Streams!
The Art and Science of UWB Antennas
, 2015, p. 289-292
Dipole Impedance and Power
The Art and Science of UWB Antennas
, 2015, pp. 282-283
Dipole Impedance

Smith-Carter Chart
Power Factor
Radial Distance (wavelengths)
Time (periods)
Harmonic Dipole
Dipole Energy
E-Field Phase Superluminal
H-Field Phase Antichronous
H. Schantz, “Near-Field Phase Behavior,” 2005 IEEE Antennas and Propagation Society International Symposium, Washington, DC, USA, Vol. 3B, 3-8 July, 2005, pp. 134-137. See:
H. Schantz, “A Real-Time Location System Using Near-Field Electromagnetic Ranging,” 2007 IEEE Antennas and Propagation Society International Symposium, Honolulu, HI, USA, 9-15 June, 2007, pp. 3792-3795.
H. Schantz and R. DePierre, “System and method for near-field electromagnetic ranging,” U.S. Patent 6,963,301, 8 Nov., 2005. See:
Charles Capps, “Near Field or Far Field,” EDN, August 16, 2001, pp. 95-102. See:
Exponential Decaying Dipole
Dipole Radiation
Superposition of Waves
Standing Waves
Opens & Shorts
Dirac's Mistake?
Photon - Photon Interactions?
Photons & Standing Waves
Implications For Physics
Energy flows in astrophysics
Energy associated with fields and waves from distant sources arises locally
EM & QM Energy Flow
EM Energy Flow Suggests Pilot Wave (deBroglie-Bohm) Quantum Mechanics
EM Waves Guide Energy
QM Waves Guide Particles
Bohmian Trajectories
Interference between two different photons never occurs.
-P.A.M. Dirac,
The Principles of Quantum Mechanics
, 4th ed. p. 9
Paul Dirac
H. Meinke and F. Landstorfer,
Energy flow in wave fields,
NTG-Fachberichte Antennen 57, 42 (1977)
Kirk T. McDonald, “Radiation in the Near Zone of a Center Fed Linear Antenna,“ June 21, 2004, updated August 7, 2012
see: (calculation by Alan Boswell)
S.A. Schelkunoff and H.T. Friis,
Antennas: Theory and Practice

New York: Wiley, 1952, pp. 124-125
Time Average Energy Flow
Energy Flow Streamlines and Antenna Design
Standard Three-Quarter Wave Monopole
Optimized Three-Quarter Wave Monopole
Energy Flow Streamlines and Antenna Design
H. Meinke and F. Landstorfer,
Energy flow in wave fields,
NTG-Fachberichte Antennen 57, 42 (1977)
Reactive Energy Flow & Physics
QM & Pilot Waves
"Electromagnetic energy flow lines as possible paths of photons"
M. Davidovic, A. S. Sanz, D. Arsenovic, M. Bozic, S. Miret-Artes
See arXiv:0805.3330v2
"Electromagnetic energy flow lines as possible paths of photons," M. Davidovic, A. S. Sanz, D. Arsenovic, M. Bozic, S. Miret-Artes. See arXiv:0805.3330v2
T. Norsen, “The pilot-wave perspective on quantum scattering and tunneling,” American Journal of Physics, Vol. 81 No. 4, April 2013, pp. 258-266.
M. Davidovic, et al, “Electromagnetic energy flowlines as possible paths of photons,” Phys. Scr. T135, 14009 (2009) [arXiv:0805.3330].
S. Kocsis et al, “Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer,” Science Vol. 332, 3 June, 2011, pp. 1170-1173.
K.Y. Bliokh, et al, “Photon trajectories, anomalous velocities and weak measurements: a classical interpretation,” New Journal of Physics, Vol. 15, (2013), pp. 1-17.
Electric vs
Magnetic Antennas
Two -20dBi ESAs
NEC 2D simulation of gain as a function of distance from PEC plane
"Electric" and "Magnetic" gain not equivalent
Combine for better multipath performance
R.D. Prosser, “The Interpretation of Diffraction and Interference in Terms of Energy Flow,” International Journal of Theoretical Physics, Vol. 15, No. 3 (1976), pp. 169-180.
Vladimir Temari:
M. Gondran and A. Gondran, “Energy flow lines and the spot of Poisson-Arago,” American Journal of Physics, Vol. 78, no. 6, pp. 598-602 [arXiv:0909.2302]
Lower Higher
Indoor Location
Electric versus Magnetic Antennas
Understanding and Designing Antennas
Understanding Diffraction & Interference
Implications for Physics
Deterministic approach to QM
deBroglie & Born (1926-1927)
Bohm (1952)
Do Photons Interfere?
Macroscopic EM waves exhibit a balance of E and H energy
Photons are quantized chunks of balanced electric and magnetic energy
Interference upsets the balance creating either virtual electric or virtual magnetic photons

Photons characterized by:
Relatively short mean free path
Relatively low drift velocity
Analogous to conduction
Planetary Motion
I can hardly imagine anyone, who knows the agreement between observation and calculation based on action at a distance, to hesitate an instant between this simple and precise action, on the one hand, and anything so vague and varying as lines of force on the other.
George Airy (1801-1891)
Correspond to how reality really works
Integrate diverse facts into a simple conceptual model, and
Lay a foundation for further progress
Models & Reality
Near-Field Electromagnetic Ranging (NFER)
Range: 20-60m
Accuracy: ~40cm-1m
Frequency ~1MHz
Capacity: ~1000 tags (540 @1Hz update) (40Hz maximum
QT-701 Tag Transmitter
QT-565 Locator-Receiver
Superposition & Analysis
What are we Ignoring?
What's Really Going On?
The Dual Nature of Impedance:
A Property of Media
A Property of Fields
Impedance Discontinuities Reflect Energy
Energy Velocity Related to Microwave Parameters

EM Energy Decoupled from Fields
Not Optical Rays
Meanders or Drifts with Collective Superposition
Typical Energy Velocity < c
What Else Are We Ignoring?
What else are we ignoring?
Solar Flux (~1kW per
square meter)
Infrared Thermal Flux
Every Other Radio Signal
The implications?
Unlikely any of the transmitted energy ends up at the receiver
Average energy velocity less than c
Reality mostly near fields and standing waves, not far fields
Opens & Shorts
Superposition of Waves
Standing Waves

Indoor Location
Electric vs. Magnetic Antennas
Understanding & Designing Antennas
Implications for Physics

Models & Reality
Fields & Energy Behave Differently
Hans G. Schantz, CTO
Q-Track Corporation

Slides - check out:
Newcastle Electromagnetics Interest Group (NEMIG)
Newcastle University
Newcastle Upon Tyne
United Kingdom

Near-Field Electromagnetic Ranging (NFER)
Range: 20-60m
Accuracy: ~40cm-1m
Frequency ~1MHz
Ease of Deployment
Capacity: ~1000 tags (540 @1Hz update) (40Hz maximum

QT-701 Tag Transmitter
QT-565 Locator-Receiver
Two Locator Receivers
170ft x 70ft
18in accurate
40Hz update
Key Advantages:
High accuracy
Fast Update Rate
Quick and easy installation
Low Infrastructure/Robust Propagation
Landstorfer, F.M., and R.R. Sacher,
Optimisation of Wire Antennas
Letchworth, England: Research Studies Press, Ltd., 1985.
See in particular Chapter 4.
Energy and fields behave differently!
Full transcript