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Part-2 Wave Phenomenon, Antennas & Radiation - Magnetism | BASIL Networks Blog BN'B

8 May, 2020

Part-2 Wave Phenomenon, Antennas & Radiation - Magnetism

Part 2: Wave Phenomenon, Antennas & Radiation - Theory and Practice
Electromagnetic (EM) Waves - A few more definitions for the Series

"We are much to accustomed to attribute to a single cause that which is the product of several, and the majority of our controversies come from that."  - Marcus Aurelius (121 - 180 )

Wave propagation is one phenomenon whose end looks like a single product, however in reality is an accumulation of many causes all having a unique contribution to the end product.  Over the centuries man has put together many mathematical and physical test to prove or disprove the cause and effect of the many controversies that have been and still are on the discussion table.

This series will answer some of the controversies and well as add new ones to continue on with the discussions, hopefully move up towards the ultimate knowledge or even better closer to the root basics of knowledge to establish a more solid foundation to grow.

Wave_Index Quick Links

Quick review to set the atmosphere for Part 2:
In Part-1 we discussed the wavelength with respect to frequency and referenced to the speed of light, Lambda=f/cwhich always raise the questions why the speed of light and in that case what is the speed of light?  To start the speed of light is a reference that has been observed in a created vacuum of the time it takes a laser beam to travel one second referenced to a 1 meter distance.  The actual derived number for the speed of light is 2.99792458 108  meters/second.  OK does that number hold true in space?  Again another controversy added to the table.  For the time being if we make this a constant, we will have the ability to change it to a variable later.  We will use this to discuss the Electromagnetic (EM) radiation phenomenon being propagated to better understand some of the parameters that determine distance the EM wave travels before it dissipates in to a non measurable entity with the instrumentation we currently have available to the public.

The frequency allocated spectrum that is compartmentalized into groups of frequencies call bands like the FM Radio BAND of 88MHz-108 MHz have been created over the years until it was realized that a standard band allocation has to be created to maintain some form of communications for growth.  So now we have a mechanism to relate the wavelength to frequency and band.  Any frequency may be represented with an associated wavelength in meters, however a band has to have a width assigned to it as the FM radio band.  The FM band falls inside the VHF band (10m to 1m)  and the actual FM band is (c/88MHz to c/108MHz) meters = 3.44 meters to 2.77 meters.  

In part 1 Introduction we also discussed the Inverse-Square Law of radiant energy from a source (GM) as defined by Equation 1.0 below.  As we see the radiant energy is reduced by the Inverse-Square of the distance from the source.

alt alt  Equation 1.0 Intensity at surface of sphere at Radius R

Authors Note:
Electromagnetic EM wave phenomenon  is the easiest subject to springboard off on a tangent while attempting to get to the root of the subject matter, only to be mentally exhausted and many times end in the same place started.  As the series moves forward we will represent EM waves mathematically only to the pint it becomes applicable to our intent of the series.  Some analysis will require linear algebra, analytical geometry and integral calculus to represent the wave phenomenon.   The objective of this series is to present EM wave phenomenon's interaction with other forces on this planet and the habitants therein.  The place that was selected to start is the planet Earth since our very existence resides on this planet Earth so what better place to start.  Understanding what has been an "experimental" exercise for the past couple of thousand years on our magnetic fields and Earth's magnetic radiation fields only tells us that we need to dig deeper.
Enjoy the series - Sal Tuzzo

What we want to cover in Part 2:
Starting a new blog series for BASIL Networks always means setting a solid foundation of reference for the series to transfer knowledge to our readers.  The intent and expectations for this series is the same for all our series - our blog's are living publications and will be updated and revised as we receive requests and contributions to the series.

The amount of scattered information on the Internet is overwhelming for any subject matter such that one could get lost just looking at content and easily loose focus on the intent of their initial search.  The issue of a infinite information library is not only where to start and more important, what is the expected results one is searching to find.  We will on occasion place a reminder on the expectations of this blog series in order to stay focused, "Author included".  The expectations for this series are to understand "Wave Phenomenon, Antennas and Radiation", the effects of radiated EM waves on materials in the waves path, frequency resonance of propagated waves influence on biological entities with respect to the Earth's radiations system.

Since this is an educational blog the intent is to cover the "boring" foundations from the recorded beginning to where we stand present day on this "Wave Phenomenon, Antennas and Radiation"   There are many physicists world wide discovering new applications as well as the home brew self educated innovators researching this "field" phenomenon which is still an experimental fact without an origin.

Lets Get Started - More Basics:
OK, Part-1 presented a lot of overview information about radiated power, radiation types, the effect radiation has on everything in our environment including humans which has triggered many questions.  We will stay focused, answer all questions, some in detailed if they are part of the presentation for the part being presented.  If the questions fall outside the current presentation we will give a general answer and present the question when the section of the series addresses the question directly.  So with that being said, lets answer some questions.

Questions & Answers
It only took a few days for the questions to come in from Part-1.  Some of the questions are a bit out of the sequence that we want to present, so we will try and keep this from running off to deep space and follow the learning progression to be able to connect all the dots.  All questions will be answered as we enter the sections they pertain to.  At this time we are still in the basic settings for the series.

Q.  What quick example would you give to show radiation exists in our everyday lives may be damaging to us?
A.  The Microwave oven, boiling water is simple and it only takes about minute.  The microwave oven frequency resides in the 2.4 GHz band and our bodies plasma is about 50% water mixed with other viscous structures makes up the delivery highway system to "every organ in the body".  The Microwave modulates the water molecule to absorb the energy causing heat which modifies its molecular structure. Today's WiFi routers also operate at 2.4 GHz band along with other Bluetooth wireless devices such as earphones, cell phones and a lots more.

Setting Basics for the Series
Setting the atmosphere for this series is a challenge since it encompasses several disciplines of engineering technologies and encourages the relationships of these multiple disciplines.  However do not get discouraged, this series will as all of our series incorporates the OBD methodology Overview, Basics, Detailed to walk you through a new experience of an ever changing field of wireless communications.  OK, lets set a Basic foundation of Given Facts that this series will reference, also for those that are very new to wave phenomenon as to set a solid foundation to relate as we move on through the series Youtube has many tutorials at all levels to bring those new to the field up to speed easily.
"If you wish to understand the universe, think of energy, frequency and vibration." - Nikola Tesla.

Immutable and Mutable Universal Laws
There two types of  Universal Laws in the universe,  Immutable and Mutable, Yeh, a ZM (Zen Moment).  That is easy enough right?   Immutable Laws as the definition or the word states are laws that "can not" be changed over time, not subject or unable to be changed, absolute.  You remember growing up and your mom says "NO."Cool   Mutable Laws are laws that are subject to change either completely or slightly and effect our very existence, you know when you talk back to your parents and you get a response " keep it up and you will experience pain".Foot in mouth   OK, now another Zen moment, if the Universe is ever changing then where do Immutable Laws exist in the Universe?  Again another controversy added to the table.  Here on this planet Earth, scientists, mathematician and physicists have empirically derived many constants that we will use in this series only "for convenience".

Convolution Theorem in Mathematics
OK, we are not going to bore you with the long version of the Convolution Theorem, just an overview.  The word convolution according to Merriam-Webster 1. :a form or shape that is folded in curved tortuous windings, 2. : one of the irregular ridges on the surface of the brain and especially of the cerebrum of higher mammals, 3. : a complication or intricacy of form, design, or structure.  OK, that doesn't sound like wave phenomenon; just another word taken from the normal language and transformed into a mathematical definition.

To convolve is to roll together to form another, so when two EM fields convolve they form a different EM field.  Convolution in the mathematics field generally usually relates to the Fourier Transforms of combined waveforms and the Fourier Transform is a way to separate the combined waveform to its singular components or frequencies.  We will use these theorems later in the series.

Brief History of Electric and Magnetic Fields
"We are much to accustomed to attribute to a single cause that which is the product of several, and the majority of our controversies come from that."  - Marcus Aurelius (121 - 180 ).  This quote or paraphrases thereof seam to be around in every class on magnetic "field theory".  The basic foundation of what is understood about magnetism and the magnetic field has many contributors from 600BC to present day and still no "what is its origin" answers even with empirical experimental facts of its stimulus-response observations over 2000 years.

The phenomenon of magnetism is currently explained to be a "field" activated in space or air by the magnet or electrical current.  However, we have no idea what a "field" could be.  It is neither space nor matter; yet, it exists within space, and is affected by, and can affect matter.  Furthermore, what or how and why does the activated "field" take on the unique shapes that it does?

Thales of Miletus - (624/623 – c. 548/545 BC) Greek mathematician, astronomer and Pre-Socratic philosopher.  Thales' theorems in elementary geometry Intercept Theorem are theorems we will use later in the advanced part of the series.  Thales' hypothesized that the operating principle of nature and the nature of matter was a single substance; "water".  His observation in 600 BC was that rubbing a piece of amber will attract straw.  Thales' was also the earliest known researcher into electricity.

Lets look at the time frame when  the "magnetic compass" was first developed in 200 BC and only took a few hundred years to the 11th century to be found useful for navigation.  From there the first recorded navigation usage in Western Europe was around 1190 up to that point the navigational sextant was used.  Things pick up in the 1700's  jumping forward in time six centuries or so.  The advancements continued on with the magnetism phenomenon when in 1785 Charles-Augustin de Coulomb published Coulomb's Law or Coulomb's Inverse-Square Law, the one we used in Part-1.

In 1820 a discovery was made by a Hans Christian Ørsted known as Oersted's Law showing the magnetic properties of an electric current in a wire.  André-Marie Ampère a French physicists and mathematician together in 1819-1820 presented electromagnetism the unity of electric and magnetic phenomenon Ampere's force law and Ampeian Loop Model and the B-Field resulted.  Michael Faraday an English scientist invented the electric motor as well as contributing to the study of electrochemistry, electromagnetic induction, diamagnetism and electrolysis.  We will present electrochemistry properties as the series moves forward to show the effects on the bio-chemistry of living cells.

Also during the 1820's two French physicists and mathematicians with alternative interests in astronomy and the other a violinist interested in vibration bodies, Jean-Baptiste Biot and Félix Savart respectively together discovered the Biot-Savart Law that describes the magnetic field generated by a constant electric current incorporating Amperes' law.  The 1800's was a decade of discovery for science and the field of electromagnetism.  This Biot-Savart Law will be presented in this part to identify the magnetic flux intensity of a point on the Earth empirically.

It is very difficult to pinpoint the actual discovery of the phenomenon, however the people involved that published the experiments and basic laws we incorporate in today's engineering and scientific research empirically represented these obversations mathematically in a way for the research and discussions to move forward. A synopsis of what was taught on science and engineering when all this started way back in the 1800's two centuries past and this magnetic field phenomenon is still being discussed.  We still do not have a suitable explanation of magnetism's  "field" origin or what it is, however we have many experimental facts of what it does and lots of mathematics to represent the experiments.  Ok, there must have been a lot happening from 600BC to 1800's AD and developed separately until the 1800's.  Well that was helpful. Cool  

A lot of stimulus-response experiments have produced several mathematical relationships that are useful in the "Space-Time-Continuum" that actually relate within the "boundaries specified" for their use.

Summary of Electric & Magnetic Fields:
The current definition of  the phenomenon of magnetism is said to be a field activated in space by a magnet or electrical current which, over the past few centuries is an experimental fact only with no idea what a "field" actually is.  It is neither space nor matter;  yet, it exists within space, affected by the space, travels through a conductor and to add to this the "field" affects all matter and also takes the form of peculiar shapes.

All the laws, Coulomb's, Ampere's,  Maxwell's, Orsted's, Faraday's and Biot-Savart all prove each other and just validate the experimental data observed.  There is no explanation of ground zero for a magnetic "field", really? yes really! there is no known scientific explanation of what it is, it just exists everywhere.  Science has represented (not defined) a magnetic field through a series of various analytical forms that represent empirical effects or a "stimulus condition" in the region around a magnet or an electric current, characterized by the existence of a detectable magnetic force at every point in the region and by the existence of magnetic poles.  This is paraphrased from several websites all lead to an experimental fact which explain many applications except the non-physical phenomenon of what it actually is and not just its experimental influence.  It is said that if you repeat a phenomenon three times the point will be understood.

Magnetism and Space
OK, for those that want to study this further beyond the scope of this blog a good place to start is Nikola Tesla and aether and Non-Physical Space.  From the notes of Nikola Tesla, "The day science begins to study non-physical phenomena, it will make more progress in one century than in all the previous centuries of existence."   "There is no energy in matter other than that received from its environment."  So this aether-space thing, has no mass, infinite elasticity, an all pervading medium of propagation of electromagnetic waves that has influence on everything.  This aether medium carrying this Electromagnetic (EM) force will continue until an opposite aether medium EM force in its path interferes with its travel.  Simple, "every action has an opposite and equal reaction", I remember reading that in a physics book somewhere.  So, now that is out of the way, lets get back to the stimulus and response of this EM wave phenomenon.  The thought to keep in mind is the aether is a transport medium for EM waves just like plasma is a transport medium for the human body, just different domains, and an EM wave will travel until it is interfered with another EM wave to either amplify, reduce or change its current effectiveness.

Earth's Magnetic field:
So now that we have a little history of how all this magnetic "field" theory came about lets look at what has been done to understand more about it.  Remembering Coulombs Inverse-Square Law in the previous section there has to be some electricity or charge flowing to produce a magnetic field and the earth supplies that charge from different minerals copper, zinc, carbon and many other ores'  that create some type of galvanic action at the various levels or layers  of the earth cores' in which the Earths Magnetic fields are generated.

OK, the convenience part shown in Figure 2.0a which is a simple sphere magnet resting permanently with its Geometric North and Magnetic North at the same point on the sphere and the flux lines are nice and neat from South to North around the sphere.  OK the not so convenient part is that Earth is not like that. In fact it is at a tilt of 23.5° East from the Geographic North Pole and the Magnetic North is also different from that by at this writing about 2.5° over the past 22 years as well.

Earths Magnetic Field, shown in Figure 2.0b, Physical North is the Magnetic South and the Physical South is the Magnetic North this definition helps the analytical process for clarification and convenience of the experiments that have been processed.  Hence: the experimental fact that unlike poles attract and like poles repel.  Also these layers of molten materials flow inside the cores at different rates depending on the characteristics of each metallurgic characteristics, size, temperature, current position of the planet and a few other parameters like plate shifts, earthquakes, all cause spikes in EM fields throughout the planet, that we will discuss later.

So the earth is a rotating sphere and it should have the same magnetic field as a magnetic sphere right?  Not really for the simple fact that the magnetic sphere is a solid and the earth's core varies in viscosity and density.  Figure 2.0a,b shows the different magnetic fields of a sphere vs Earths measured magnetic fields from the IAGA (International Association of Geomagnetism and Aeronomy) data table measured and recorder every 5 years created collected data is called the International Geomagnetic Reference Field. The (IGRFddd) tables where ddd is the tables reference and are downloadable and plotted to the following Figure 20.1b.  The IGRF2015 Table lines in Figure 2.0b was created from data gathered from orbiting satellites and other geomagnetic instrumentation around the globe.

IMAGE_MagneticField-EarthScale.jpg
Figure 2.0a. Rotating Spheres' Magnetic Field ω = x

alt
Figure 2.0b. Earth's Magnetic Field IGRF Table2015

       Figure 2.0 [a, b]   Rotating Sphere Magnetic Field vs Earth's Magnetic Field

So looking at Figure 2.0b we see that the magnetic fields of the earth are quite different and using deductive reasoning with the understanding that the earth's core is not a fixed stationary solid on a fixed axis, would only stand to reason that the magnetic fields would change according to the earth's motion in order to find its equilibrium.  Also note that the earth is tilted about 23.5 Like riding a bike for the first time and warbling a bit until you get your balance.  By the same deductive reasoning the Earth's magnetic fields would also have several motions or paths of varying frequencies and amplitudes around the planet that makes up these different fields.  The Earth has multiple frequencies of different amplitudes for the very fact that the core is always in a state of continuous movement and is continuously changing density and its core viscosity while spinning on its axis of 1 revolution every 23 hours 56 minutes 4.1 seconds as well as spinning around the sun within our solar system.  Our solar system is also spinning around the galaxy our solar system resides in.  So for the time being lets remain inside the living atmosphere for our species on the Earth.

The experimental data from the surface of the planet globally has been plotted in three graphs, the magnetic radiation intensity, the Inclination and the Declination from the point of reference which is magnetic North.  The magnetic poles that form the Earth's magnetic fields are dipolar that is the poles do not coincide, hence: Physical North is Magnetic South and Physical South is Magnetic North.  The compass needle has two poles north and south, if the compass always points north then the needle that is pointing north is really magnetic north, this is called the horizontal intensity component of the magnetic field.  So the Earth is like a big cement mixer rotating and shifting the core mixing everything up and creating multiple flux lines that also vary as it travels through space linked to our solar system.

The Inclination component of the map shows lines that vary from -90 degrees (up) to +90 degrees (down) where 0 is the equator mark.  The Declination component is the displacement of the true magnetic North from the Geophysical north.  The Declination or the magnetic north shift over time has declined about 2.5° over the past 22 years.  The Declination component is a positive eastward deviation relative to true north represented as an angle relative to magnetic north and true north.

As we stated many physicists and mathematician participated in the empirical experimentation and all have their own references to label the field strength as the Table 2.0 below shows the various field names cross reference;

Value Symbol Parameter To Parameter

  Value

1 SI Gamma Weber/meter2 1.00000000E-004
1 B Gauss Weber/Inch2 6.45160000E-008
1 L/cm2 Line/cemeter2 Weber/centimeter2 1.00000000E-008
1 M/in2 Maxwell/inch2 Tesla 1.55000310E-005
1 M/m2 Maxwell/meter2 Weber/centimeter2 1.00000000E-004
1 T Tesla Maxwell/inch2 6.45160000E+004
1 W/cm2 Weber/centimeter2 Line/cemeter2 1.00000000E+008
1 W/in2 Weber/Inch2 Gauss 1.55000310E+007
1 W/m2 Weber/meter2 Gamma 1.00000000E+009

 Table 2.0  Converting Values and Labels for Convenience

The Intensity of Earth's magnetic fields varies from around 25µT around the equator and around 60µT at the poles, Figures 2.1, 2.2, 2.3 and 2.4 represent the magnetic fields components magnetically, North, South, East, West for a selected point on the planet and shows how the planet core changes in magnetic field intensity.

The Earth's rotation both on its axis and its orbital rotation around the sun influences the random earth quakes and tremors recorded by seismic sensors positioned globally through globe.  Data collected from these sensors are shared through a world scientific collaboration and available to the public for research.  The following data and images are referenced to the National Oceanic and Atmospheric Administration  Center For Environmental Information (NOAA NCEI)  NOAA NCEI.

alt
Figure 2.1  Earth's Magnetic North
2019 Declination
Obtained from NOAA NCEI/CIRES Model

EarthsMagFields-IntensityScale.jpg
 Figure 2.2  Earth's Magnetic Field
Intensity 2020 Map
obtained from NOAA NCEI

alt
Figure 2.3  Earth's Magnetic North
Inclination 2015 Map

obtained from wikipedia

alt
Figure 2.4  Earth's Magnetic Field
Declination 2020 Map

Measuring  Earth's Magnetic Filed's:
OK, now that we have a small overview of the magnetic field phenomenon showing it is all around us in this thing called air space we will now get down to the observations that have been recorded by the physicists and the laws that have been presented.  I know to some that this may be boring, however we will be using this throughout the series when we get into the wireless radiation and its effects.  Yes, learning behavior is so unpredictable and always has been for our species.  Sometimes those that have not been exposed to a field of interest give us some of the most advanced observations that the experts sometimes overlook, it is called being human.  If you got this far reading take a deep breath - we are not going to cover equations like Maxwell's laws etc, that is for the math class to cover and explain, however we will cover the Biot-Savart law (effectively Maxwell' 4th equation) since it is the easier of all the laws and ends up with a simple algebraic equation that we can just plug in the numbers.  The construction of a Tangent Galvanometer is quite simple to assemble and is relatively inexpensive, less than $12.00, we will take pictures in the next part of the series.

Since this is magnetic field phenomenon is still in the experimental arena since a "field" has only been explained as an experimental fact showing these experimental facts via the Earth's magnetic fields we will now incorporate these magnetic law relationships and link the Brief History of Electric and Magnetic Fields in the previous section to a real world application.

Figures 2.0 through 2.4 show the Earth's magnetic field measurement components we will take the walk through how these field maps came about.  Every first year physics student has seen this performed many times in the classroom so, this make for a great example and the Internet is full of video examples all giving their own interpretation of this measurement with equivalent results.  

OK, A galvanometer is basically an ampere meter like Figure 2.5a above that measures current through a wire by displacing a rotating coil needle inside a "fixed" permanent magnet depending on the electromagnetic field the current produces in the coil needled wire.  The Tangent Galvanometer is a device that allows the creation of an electromagnetic field intensity that is equivalent to the magnetic intensity field being measured.  In the previous section the laws set for convenience mathematically move domains from magnetic field and electric current in order to satisfy and prove each others laws, which they do.  So since several physicists-mathematicians introduced different observations,  created laws explaining their observations and they all ended up proving each other's law, it is at this time by experimental fact safe to use them in our analysis here on Earth at least.  One note about the Tangent Galvanometer is that the wire size used for the coil and the number of turns have an influence on the actual intensity of the field.  This is due to the wire resistance and length that will effect the current supplied and the magnetic field produced by the wire and measurements outside the center of the coil will be influenced.

Now that we have an overview of the Earth's Magnetic fields from Figures 2.0 to 2.4 we will walk through the experimental exercise of just how the magnetic field intensity is measured at a point on the Earth.  The Galvanometer and the compass have been around for some time when the Tangent Galvanometer was created to understand more about the magnetic North and the Geographic North pole.  The Tangent Galvanometer measures a point of magnetic intensity tangent to the fields flux line geometry; the point tangent to the flux line has both magnitude and direction which makes it a vector.

alt
Figure 2.5a  D'Arsonval Galvanometer Permanent Magnet
and rotating coil needle movement

alt  
Figure 2.5b  Sine and Tangent Galvanometer
Claude Servais Mathias Pouillet (16 February 1790 – 14 June 1868)

The Tangent Galvanometer was designed by Claude Servais Mathias Pouillet (16 February 1790 – 14 June 1868) and still is in use today by colleges and universities and the industry although the manufacturing is a bit modernized and simplified.  The technology has advanced to the level that a single Integrated  circuit gives all three intensities x, y, and z in Tesla's.

Figure 2.5b  shows the Sine and Tangent Galvanometer made around 1850 in Paris by Ruhmkorff after plans by Claude Pouillet.  It consists of a non-magnetic ring with 10 to 100 turns of wire where a current is placed (I) generating an electromagnetic field (B) to be equivalent to the intensity of the magnetic field B(r) being measured and a compass resting in the middle.  The round hollow part of the device contains a fixed number of turns (N) of a fixed wire size diameter dl in meters and acts as a toroid that generates a magnetic field that is referenced at the center of the toroid.

So, the first step is to represent the different Magnetic components of the Earth. This is shown in Figure 2.6 that represents the magnetic vector components of a single point of the Earth's magnetic field and will be used to mathematically represent the magnetic Intensity.

The Earth's Magnetic Components:
Before we jump too deep lets look at the magnetic components of the planet Earth as shown in Figure 2.6 Earth's Magnetic Field Components as to get a pictorial of the interaction of these vectors.  The process to obtain the magnetic field intensity at a selected point on the Earth using the Tangent Galvanometer such that we are able to calculate the intensity vector r'  shown in Figure 2.6 is simply generating an equivalent magnetic field using the coil in the Tangent Galvanometer that will emulate the geometry of the field at a point tangent to that field, simple.

The Tangent Galvanometer only allows us to obtain the horizontal magnetic field pointing to the Magnetic North at the point of measurement which is the adjacent to the angle of inclination this is the horizontal or parallel component of the Earths magnetic field at the point of measurement.  Since the tangent point contains a magnitude and direction from the point of the measurement this forms a right triangle that contains the angle of inclination as shown in Figure 2.6.  The point of measurement latitude, longitude and inclination angle gives us the magnitude and direction, the hypotenuse of the right triangle r for the point we want to measure.

alt
Figure 2.6  Earth's Magnetic Field Vector Components Summarized

To measure the Earth's magnetic field Intensity at a point lets list the Givens, Measured, Controlled and Finds to setup the process.

Given:

    Latitude, Longitude = Point to be measured
   Area of circle:    alt
   Circumference:   alt 
   alt  Permeability constant

Tangent Galvanometer:
     Coil Size in Meters = 0.16256  (6.4 inches)
     Number of Turns of Coil = 15 Turns
     Wire size = 16 AWG = 0.058" = 1.29 mm

Measure:
    Inclination Angle at Measure Point Lat,Long

Controlled:
     I = Applied Coil current in Ampere's
           Current to move Compass N 45º East

Find:
     alt Magnetic Field of the Horizontal  (Parallel Component)
               generated by the coil current.

    Magnetic Field B at MP (Measurement Point)

Measure:  Inclination Angle alt  for the vector at the point of measurement.

Since we will be creating the horizontal (parallel) magnetic flux component using the tangent galvanometer we will require the Inclination angle that the magnetic field is at.  This is easily obtained using a compass on a flat surface recording a fixed point A degrees then rotating it 90º towards the east an record the angle B the needle moves as shown in Figure 2.7.  The Inclination angle is A+B = Angle in Degrees.  This allows is to calculate the actual magnetic field strength of the point of measurement, we will get to that shortly.

alt

alt

Figure 2.7  Measurement of Angle of Inclination Using A Compass

Step-1
Remove all current from the coil of the Tangent Galvanometer and align the north to be in parallel with the coil as shown in Figure 2.8.  Then place the Tangent Galvanometer at a right angle to the surface and measure the angle of inclination (alt ), record this angle in degrees and return the galvanometer to its upright position and check to see if the compass is still horizontal to the coil as shown in Figure 2. 8.

alt
Figure 2.8  Top View of the Tangent Galvanometer for Step 1

Step-2
Apply a current to the coil that will move the compass needle to 45° (NE)  as shown in Figure 2.9 and record the current applied to the coil.  At this point the Magnetic North is equivalent to the magnetic field we are attempting to measure.  For this experiment we are referencing the point to measure from the center of the wire loop which creates a symmetry that all the current elements contributions around the loop add directly at the center. The current in the loop produces a magnetic force equivalent to the MP at the center of the loop equivalent to the Magnetic North which is used to compute the parallel flux line force that is obviously parallel to the flux line of the point we are measuring at the center of the Galvanometer loop.  The intensity tangent to the flux line is at the inclination parallel to the flux line as shown in Figure 2.10a and the vector is shown in Figure 2.11.

alt
Figure 2.9  Top View of the Tangent Galvanometer for Step 2

Step-3
Record the number of turns setup on the Tangent Galvanometer (N = 15).  The one we will use has a selection of 5, 10, 20 and 35 turns.  We will select the 15 turns connections.

Step-4 
Measure the diameter of the toroid coil of the Tangent Galvanometer in meters (2R = 0.16256 meters (6.4 inches)) for our Tangent Galvanometer we are using a 6.4 inch ABS pipe 3/4 inches long to wrap 16 AWG copper laminated magnet wire 15 turns.

Biot-Savart Law Applied
The Biot-Savart Law is only one of many laws that have been created empirically to show a magnetic energy "field" exists from applying an electric current in some way or another.  We will apply this law to measure the magnetic force for a point on Earth.  This technique is applicable to other magnetic measurements as for a bar magnet, a circular magnet and other forms of magnetic generation.  The law applies when analyzing a magnetic "field" to its Magnitude, Direction, Length and proximity to the source of the energy field.

It is an interesting point of why the Galvanometer wire loop was selected instead of the typical coil, Figure 2.10a and Figure 2.10b show the differences in magnetic fields of a wire loop and a wire coil.  The wire loop allows us to use the Tangent galvanometer to actually measure an unknown field and creates a symmetry since all contributions are added at the center of the wire loop and is the same throughout the loop makes for a unique condition for analysis mathematically using the Biot-Savart Law.  The coil in Figure 2.10b the main magnetic field is in the center of the coil which is normally configured for a solenoid with a magnetic rod in the middle since the majority of the magnetic field is in the center of the coil and has weaker fields outside the coil.  The more turns on this type of configuration the stronger the magnetic field strength will be.

This is not rocket science level however it is important to the series since we will be referencing it when we get into other radiation methodologies created by a current.  Lets look at the magnetic field of a loop of wire as shown below in Figure 2.10a and the vector representation in Figure 2.11 as we see the most intense field is in the center of the coil, as the field expands around the coil the field is weakened until it blends with the Earth's magnetic field and blends in as part of it.  An interesting note is that depending on the wire size and form the magnetic fields will reshape to that form.

alt
Figure 2.10a Magnetic Field Wire Loop

    alt

 

    Figure 2.10b Magnetic Field Wire Coil

Magnetic Fields of the Tangent Galvanometer Wire Loop and a Solenoid Coil

There are three components that influence alt at the Measurement Point (MP) and they are a. I the current in the coil, b. alt the parallel field intensity create by the current in the coil and c.  alt the inclination angle direction of the field we are measuring as shown in Figure 2.10b.  MP the measurement point,  is tangent to the loops magnetic field created from I, the coil current where as altis that magnitude and direction of Earth's Latitude and Longitude given point we want to measure.  The intensity alt orthogonal to the parallel field does not contribute since it is at (90°) and the scalar components point in different directions perpendicular to the axis and the complete loop is 0 due to the symmetry where all field contributions add at the center of the loop this is a unique case in the geometry for the Tangent Galvanometer.  The alt component then becomes the circumference of the wire loop alt.  Only alt contributes to the total intensity B at point MP being along the parallel flux line axis of the loop.  The symmetry created from the current applied to move the compass needle 45° creates the symmetrical magnetic fields that is equivalent to the field point tangent to the current I flux line being measured and the inclination angle alt will give the direction.

alt
Figure 2.11  Vector Representation of the Tangent Galvanometer Wire Loop Setup

So for the different contributions, the Tangent Galvanometer and the current applied to coil produce the equivalent magnetic field strength of the magnetic north (alt ) is given as the Biot-Savart Law as Equation 2.1 below.  The only contribution to obtaining B is integrating alt which is defined as:

alt

The current I contribution to MP to calculate B for the point in question is given when we adjust the current to move the compass 45° NE in Figure 2.11.  This sets the equivalent magnetic field at the on the parallel plane of the Magnetic North for the MP point in question due to the symmetry of the flux lines and the sum of all the components are added at the center of the wire loop.

The next step is to incorporate the Biot-Savart Law to obtain the magnitude and direction of B at the MP latitude, Longitude given along with alt  the inclination angle.  From Figure 2.11, we can derive the parallel contribution as alt =  altcos(alt )  then the magnitude of the intensity is defined as altalt / cos(alt ).  Applying Boit-Savart Law for the parallel contribution becomes:

alt

Equation 2.1 Biot-Savart Law
alt is basically the circumference of the wire Loop

alt  

 Then:alt

Evaluating the Integrals  alt, alt (Big Jump forward for convenience)
From the Givens above we have:
N = Number of turns of the loop, The       
circumference just increases by N
I = Current applied to the loop in ampere
alt = Inclination xx
° of Latitude, Longitude

alt

Equation 2.2 - Parallel (Horizontal) Field

alt

Equation 2.3 - Total  Intensity at inclination alt

OK, to test this go to Goggle map and set your location and get the Latitude, Longitude from Goggle map and enter them into the NOAA NCEI calculator, (NOAA site also allows you to enter a physical address as well) that will give you all the magnetic field information of the Lat, Long you entered. The result is a table similar to Figure 2.12 below.   Of course you will require a tangent galvanometer, which we will be building for the next part of the series.  They are very easy to build and all the parts are under $12.00 all locally obtained for those that want to build their own to follow the series.

alt
Figure 2.12  Magnetic Field  32.423831, 110.995709

OK, now that we have an understanding of the Earth's magnetic fields lets see how this will help us out with the IoT Core Platform Development.  Over 20 years ago Honeywell corp released a device to the public that would measure magnetic fields down to the micro-Tesla levels on a small integrated circuit.  Today you can purchase these IC's for under $2.00, also several manufacturers have used these devices to perform 3D magnetic field measurements of a point X,Y,Z from an EM source.  We will present these devices when we move forward with the Interface for the IoT Platform.  The industry advanced to a technology level that these Magnetic field sensors are used in so many places side by side with GPS devices, manufacturing process control systems and more.

SUMMARY
OK, this was a long exercise for this part of the series and if you are wondering why we went through this exercise and what does this have to do with Wave Propagation, Antennas and radiation, well it is simple.  The Earth is a continuous source of magnetic radiant energy in this place we call space and has a direct effect on all life forms on this planet.  The Earth also has magnetic oscillations or frequencies that are unique to its structure and to understand the Earth's magnetic frequencies and forces we have to start at the real basics of what science already knows from experimentation.  The Magnetic radiant frequencies are important to all life forms on this planet and as we move forward we will see how interfering with these frequencies disrupts the resonance of life forms as well.  This will also set as a reference of radiation or EM waves that are healthy to all life forms as well as to give a brief overview of what is ahead in this series.  Our point here is to understand that the magnetic "fields" vary as a function of Energy, Frequency and Vibrations and the best that science has to offer at this time are mathematical representations from empirical evidence.

So from this part we have shown that a EM field is generated from a constant current and it does transmit for a distance in air-space.  This would be the same if the current was oscillating at a frequency bands which we will get to in this series.  Also we see that the field energy is reduced as we move further away from the source current generating the field.  It is difficult to discuss magnetism without mentioning at least one of Maxwell Laws since Maxwell combined many of the different electromagnetic laws into basically four laws and what we presented here was a version of the fourth law.

We are constructing a few of the Tangent Galvanometer for our lab measurements later in the series at different transmission frequencies up to 100GHz in order to measure the radiation at specific points of transmission path since many of the EMF meters today on got as high as 8GHz a couple up to 10GHz.  The construction plans will be presented as the series moves forward.

As the series progresses the author, Sal Tuzzo will be available for discussion through the BASIL Networks Contact Form for those that want to apply this series to conduct their own experiments.  The Author is always be appreciative for the private comments sent through the contact form for suggestions and advice during the development of this series.  This is a growing opportunity for everyone entering into RF product development arena as well as a great review for us "well seasoned" in the field to just refresh our human DRAM (Dynamic Random Access Memory).

It is recommended for those that have specific questions on the series to use the BASIL Networks Contact Form to separate them from getting lost in the general comments for each blog presentation.  For all specific design request or contracts please feel free to contact us.


Part 3...n  Preliminary Outline for the series "Basic Wave Phenomenon Antennas & Radiation" -Continued
There are many more Laws of energy transmission in the wireless arena that will be addressed as the series progresses showing the relationships between them and how they relate to the wireless communications as they are applied today.  Energy distribution laws we will address are:  Planks Law,   Stefan-Boltzmann Law,  Maxwell-Boltzmann Distribution Law,  Wien Displacement law,  Emissivity,  Kirchoff's Law,   Lambert's Law also know as the Beer-Lambert Law,  So as we see there are many theories that have been experimented with however, with all these laws there are still anomalous deviations that seem to fall outside the norm which we will discus later in the series.


Wave_Index Quick Links


Reference:
The books in these references are my Northeastern University college of engineering text books except for the Ultra-High-Frequency Techniques, that was a gift from a colleague.

Ultra - High - Frequency Techniques (1942  D. Van Nostrand Company)
    J.G. Brainerd,  Professor EE Univ. of Pennsylvania
    Glenn Koehler, Assistant Prof. EE Univ Wisconsin 
    Herbert J. Reigh,  Prof. EE Univ. Illinois
    L.F. Woodruff, Assoc Prof. EE  MIT Massachusetts

Wave Propagation and Antennas (1958 Library of Congress: 58-9431) by George B. Welch Professor of Physics Northeastern University and Professor Hollis S. Baird whom I have had the honor of being one of his students.
Basic Microwaves (1966 Library of Congress: 65-16814) Bernard Berkowitz
Physics (1966 -ISBN: 0 471 71715 0) Robert Resnic and David Halliday Part I
Physics (1960 -Library of Congress: 62-15336) ) Robert Resnic and David Halliday Part II
Fundamentals of Physics  Revised Printing (1974 ISBN 0471-34431-1) Robert Resnic and David Halliday
Signals in Linear Circuits (1974 ISBN 0-395-16971-2) Jose B. Cruz and M.E. Van Vlakenburg

Wikipedia - On-Line Knowledge Center


Publishing this series on a website or reprinting is authorized by displaying the following, including the hyperlink to BASIL Networks, PLLC either at the beginning or end of each part.
BASIL Networks, PLLC - Wave Phenomenon, Antennas & Radiation Part-2 Electromagnetic (EH) Waves-A few more definitions for the series: (May 8, 2020)

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[Sal_TUzzo]

Sal (JT) Tuzzo - Founder CEO/CTO BASIL Networks, PLLC.
Sal may be contacted directly through this sites Contact Form or
through LinkedIn

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