Electromagnetic radiation 
 -----------------------
    In 1864 Maxwell formulated his theory of electromagnetic radiation 
(EMR), tying together the then separate studies of electricity and 
magnetism. Maxwell believed a real medium was necessary for conveying 
the EMR. Later, by Einstein, such requirement was proved false. EMR 
can travel thru empty space and it is by it that we acquire virtually 
all intelligence about the universe. 
    The amount of knowledge we get by meteorites, cosmic particles, 
Moon rocks, solar wind, and the like is minuscule against the 
information from the EMR. Or, in reverse logic, with no EMR our 
awareness of the universe would be pretty much zilch. 

Frequency versus Wavelength
 -------------------------
    We employ either wavelength or frequency to describe EMR. lambda 
is the symbol for wavelength; nu, frequency. Letter f is also commonly 
used for frequency. The two are interchangeable at will by 

 c = lambda * nu 

 +----------------------+ 
 | FREQUENCY-WAVELENGTH | 
 | RELATION             |
 |                      |
 | c = lambda * nu      | 
 +----------------------+
    The metric name for 'cycle per second' is 'hertz' but many older 
scientists still use cycles/second. Some works actually use 'sec^-1' 
to clarify this idea, like '92e6 sec^-1'.                         
    The metric unit of wavelength is a multiple of the meter like 
nanometer in the optical range or micrometer in the infrared zone. The 
micrometer is prevalently stated by its older na,e 'micron'. 
    Because it's clumsy to write the formal symbol for 'micro-' as the 
letter 'mu ', the letter 'u' is sometimes used. It kind of looks like 
a 'mu'.. 
    In astronomy an older unit, 1e-10 meter or angstrom is still in 
wide circulation. 1 angstrom is 1/10 nonometer. 
    The choice to use is often a matter of tradition. Some regions of 
EMR were explored as a function of wavelength and others of frequency. 
Radiowaves are generally described in frequency while light is cited 
in wavelength. We can use either one as we like for any region of 
electromagnetic radiation. 
    The EMR comprehended between two limits of wavelength (or 
frequency) is called a spectrum, after the visual apparition 
discovered by Newton in his experiments on light. He saw, when letting 
sunlight refract thru a glass prism, a splay, devolution, dispersion 
of colors. Much later these were found to be the multitude of 
wavelengths represented in sunlight, each refracted slightly 
differently thru the prism. Our eyes register each wavelength as a 
separate color. 

Irregular jargon 
 --------------
    along with the separate work in the various wavebands of 
electromagnetic waves comes the inconsistent jargon describing the 
waves. altho I here use the International system of units and terms, 
you will read and hear other terms, words, units of measure. 
    The main alternative measurement system is the CGS, 'centimeter-
gram-second. Irs units are still in wide use, mainly in specialized 
sciences. The units are mostly powers of ten multiples of SI units, 
making translation reasonably easy. 
     Terminology, names, nomenclature is more varied, with terms in 
one waveband having different meaning in an other. You do have to 
study the jargon when working across wavebands.A common instance is 
the designation of wavebands. There are no official boundaries between 
the zones of wavelength, except for certain ones regulated by 
government agencies, such as broadcast radio. It happens that one 
scientists calls  the band he works with 'far ultraviolet' but an 
other scientist in his own work calls it 'soft X-ray'. 
    An other situation is that many combinations of units, in both CGS 
and SI, have honorary names, like 'joule' for 'newton.meter' and 
'volt' for 'newton.meter/coulomb'. 'newton' is itself the honorary 
name for 'kilogram.meter/second2'. Most of these names honor 
scientists who worked with associated principles, effects, concepts. 

Electric charge 
 -------------
    The elemental unit of electric charge is the electron. Irs charge 
by history is 'negative' of strength one unit. The proton also carries 
one unit of charge, this being 'positive'. charges of like signum 
repel and those with opposite signum attract. In ordinary matter the 
protons and electrons are equal in number, netting the overall charge 
to zero. 
 The protons are locked in atomic nuclei and are not easily available 
for useful work. The electron can move around among atoms to 
accumulate static charge or become an electric current. 
    A body taking on a negative charge has an excess number of 
electrons. The protons in the target are too few to net out all the 
electrons, leaving the extra ones to give the body its net negative 
charge. 
    A positively charged body has a decess of electrons, leaving the 
extra nuclear protons to exert a net positive charge. 
    Transferring electrons to and from an object was primitively done 
by rubbing the object with silk or fur. Certain materials gained 
electrons to be negatively charged. Other lost electrons to be 
positively charged. This effect is the practice of electrostatics or 
static electricity, still in routine use for entertainment. 
    A charged body creates an electric field around it that presses an 
force on test particles in the field.
     Priestley in 1766  experimented with charged metal  cans. He 
found that within the can there is no electric field and correlated 
this fact with gravity. Within a hollow  vessel there is no gravity 
field from the vessel's own mass. 
 This effect comes from the inverse-square law. of gravity. Charges 
must also follow the same rule. 
    Coulomb in 1785 built a torsion balance, like the one from 
Cavendish for gravity, to determine the force relation directly. 
  Coulomb verified Priestley's work and found that 

    force = K * charge1 * charge2 / distance^2 

    charge1 and charge2 are the two charges, with their positive or 
negative signa. If their product is positive (+ times + or - times -) 
the force is repulsion. A negative product (+ times -) is an 
attraction. 
    The unit of charge was is primitively the electron but this is a 
in infinitesimal unit. The SI unit is the Coulomb, equal by 
experiment and measurement to 

    1 coulomb = 6.4518e18 electrons 

    K is the Coulomb constant like the Newton constant.It was a single 
number under older systems of units. In the SI it is diffracted into 
 
    K = 1 / (4 * pi * epsilon)

to coordinate with other electromagnetic units. epsilon is a property 
of the neduyn carrying the electric field. 
    Today we start with the definition of electric current, with unit 
ampere. The electric current flowing thru an electrical device is 
marked on device's nameplates on electric devices as a flow of 
electricity thru the device. 
    The ampere is 

    1 ampere =  1 coulomb/second 

Batteries are sometimes specified by thee ampere.hours of charge they 
hold. With 3600 seconds per hour, 

    1 ampere.hour = 3,600 coulomb 

    Before the electron was discovered as the sole charge carrier in 
electricity, we spoke of the electric  fluid flowing from the positive 
charge to the negative charge. This convention embedded into the 
nascent 19th century electrical industry and persists today. 
Electricity flows from the positive end of a battery to the negative 
end. 
    The flow of electrons ended up by luck being the opposite flow, 
from negative to positive. This is part of electronics, developed in 
the early 20th century. 

Electric field
 ------------
    An electric charge has around it an electric  field. It is similar 
to the gravity field around a mass. The electric field  of a point 
charge follows Coulomb's inverse-square law. 

  force = (1 / (4 * pi * epsilon)) * charge1 * charge2 / distance^2 

    In a way analogous to Newton's gravity field strength, a charge q1 
sets up an electric field of strength E at distance r 

  (field strength) = (1 / (4 * pi * epsilon)) * charge1 / distance^2  

    epsilon for a vacuum has the smallest value of all media and is 
given the symbol epsilon0. Its value is 

epsilon0 = 8.854e-12 C2/N.m2. 
    The 4*pi factor is an effort to simplify calculations like for 
illumination. It didn't work as hoped but we're stuck with it. 

 +-----------------------------------------------+ 
 | COULOMB'S INVERSE SQUARE LAW                  | 
 |                                               | 
 | F is force, E is field strength, q is charge, | 
  | r is distance                                | 
  |                                              | 
 | F = (1 / (4 * pi * epsilon)) * q1 * q2 / r^2  | 
 |                                               | 
 | E = (1 / (4 * pi * epsilon)) * q1 / r^2       | 
 |                                               | 
 | epsilon0 = 8.854e-12 C2/(N*m2)                | 
 +-----------------------------------------------+ 

Magnetic poles and fields 
 --------------------- 
    It turns out that there is little need for a distinct parameter of 
a magnetic pole strength. This would be symmetrical with the unit of 
electric charge or of mass. Because wo can not actually have separate 
magnetic poles and the whole purpose of magnets is to build a magnetic 
field in a given volume, work is performed with just the magnetic 
field strength. An other reason  is that magnetic fields can be 
created via electromagnets. There generally are no 'poles' in the 
ordinary sense. In Ampere's law the magnetic field surrounds th wire 
in closed loops. There is no actual 'poles'. 
    In history, Michell in 1750 did discover the inverse- square law 
for magnetic poles. His equation parallels those for gravity and 
light. (Priestley and Coulomb were still in the future.) 

    magnetic force = M * pole1 * pole2 / distance^2 

where M is  the Michell constant. No value is standardized for it 
because we hardly ever use this inverse-square formula. 
    pole1 and pole2 are magnetic poles, north or south. Like poles 
repel; opposite, attract. From the absence of separate magnetic poles, 
there is  no standard value for a pole strength. 
    It could be feasible to experiment with Michell's law with a long 
bar magnet and keeping close to each end of it. This dilutes the 
influence of the other end on the force. 
    The magnetic field strength is found by the action of the field on 
a test electric current. In a lab setup of specified geometry and 
operation within the magnetic field. The force on the apparatus is 
measured. We have 

     (magnetic field strength) = func(force, current, geometry) 

The result of such an experiment is that the magnetic field strength 
is in newton/(ampere.meter). Note this incorporates the main factors 
defining field strength: newton for force, ampere for current, meter 
for geometry. 
    This is hardly symmetrical with the newton/coulomb units 
for the electric field strength. Given the lack of separable magnetic 
poles we are compelled to go thru this round-about definition. 
    The units newton/(ampere.meter) is the tesla. The CGS unit, gauss, 
is still widely use. 10,000 gauss equal one tesla. The Earth's 
magnetic field strength at ground level is 1/2 to 1 gauss or 5e-5 to 
1e-4 tesla. 
    Aren't we engaged in circular reasoning? We first used a magnetic 
field to define the ampere, the coulomb/second. Then we use the ampere 
to define the magnetic field! In a way, yes, and philosophers debate 
this feature of physics endlessly. For one thing it leaves us with no 
explicit quantity for the strength of a magnetic pole!  

Ampere and Fraday 
 ---------------
    In the early 1800s there were hints that electricity and magnetism 
are somehow linked. Oersted and also Ampere in 1820 discovered that an 
electric current can produce a magnetic field.     Connect a wire 
across a battery, source of electric current, with a small lamp bulb, 
like fro a pocket torch. The lamp shows that current is flowing and 
prevents the battery from discharging by a short circuit thru the 
wire. 
     Put a scouting or hiking compass near the wire. The compass 
deflects away from its normal alignment to magnetic north. Every where 
along the wire the compass reacts this way. The electric current 
generated around the wire a magnetic field that attracts the compass 
needle. 
    When the circuit is opened, the current stops, the magnetic field 
vanishes. The compass returns to its natural alignment. 
    In words Ampere's law is 

    (electric current)_ -> (magnetic field) 

where '->' means 'can produce or generate'. 
    Faraday in 1838 found that a varying magnetic field can produce an 
electric current. Connect the wire to the lamp bulb this time with no 
battery..Sweep one end of a bar magnet over the wire.The motion of the 
magnet changes its field along the wire. 
     As long as the magnetic field is varying, bu continuing to move 
the magnet. an electric current flows in the wire and lights the bulb.  
The bulb may glow weakly but a stronger glow is obtained by more 
vigorously sweeping the magnet. . 
    When the magnet is removed or held still, the current stops. The 
galvanometer shows zero flow. 
    A verbal statement of Faraday's principle is 

    (varying magnetic field) -> (electric current) 

Note carefully that Ampere and Faraday laws are not symmetrical. While 
a steady electric current produces a magnetic filed by Ampere, it 
takes a changing magnetic field to make an electric current for 
Faraday. A steady field does not yield electricity. 
    Faraday's principle quickly leaded to the invention of the 
electric dynamo or generator. Until then elecctricity was made by 
chemical batteries or by static charge. In a dynamo a coil of wire is 
rotated within the poles of strong magnets. As the coil rotates it 
'sees' a varying magnetic field and a current is impressed in it. This 
current is drawn off to run machinery. 
    Such dynamos were built by the 1860s for on-site production of 
electricity, like in factories and ships. The coil was rotated by 
steam engines or water wheels. 
    By way of history, Edison did not 'invent electricity'. Edison was 
the first to commercialize electricity for anyone to obtain its 
benefits. In doing so he invented the electric service industry. 
Edison's original company from 1882 is today's Consolidated Edison 
Company of New York. 
    The discoveries by Faraday and Ampere was elaborated into 
mathematical expressions, skipped here, as new laws of physics. 

Lenz effect 
 ---------
    If under Faraday's law a magnetic field induces an electric 
current, doesn't that current in turn under Ampere's law set up a 
magnetic field? If so, can these two fields combine to produce more 
current? And we could bleed off some of this current to run our 
machinery without further input of energy to the wires! 
    Is this a perpetual motion machine in the rough?
    No. 
    The resultant field set up by the electric current opposes the 
stimulant field  to temper the rate of change. The fields are 
antagonistic, not sympathetic. 
     You may experience the Lenz effect with the wire and lamp. With 
the circuit open you can freely sweep the magnet over the wire. When 
the circuit is closed you feel resistance against the magnet. This is 
the Lenz field opposing the magnet. 
    This is way a dynamo needs a continuous external force to keep the 
magnet-coil moving and maintain the output of electricity. 

 Lines of Force 
 ------------
    A line of force associated with a field is not a real physical 
feature in nature. Older texts sometimes spoke of lines of force as if 
they were actual traces thru a field. 
    None the less they are an excellent aid for visualizing fields and 
they in fact do have a physical foundation. A line of force is the 
trajectory of a test particle placed in the field and released to move 
under the force of the field. It's like a freefall trajectory in 
astrodynamics. There is no initial velocity of the particle. The 
particle is gently let go in the field, not or injected or propelled. 
    For an electric filed we use a positive charge, like a proton. 
When released in the field it is repelled from other positive charges 
and attracted to other negative charges. 
    The path of this particle is a line of force. In principle you can 
actually  map out the field.
     The direction of motion of the test particle is commonly 
indicated in diagrams by arrows along the line. We can speak of a line 
'going from positive to negative' as a jargon, not a statement of real 
movement of the line itself. 
    The number and density of lines of force qualitatively show the 
strength of the field. More and denser lines indicate a field stronger 
than where the lines are spread apart. The number of lines emanating 
from or cascading into a charge qualitatively is the strength of the 
charge. Stronger charges have more lines associated with them. 
    We can not actually place a magnetic pole into a magnetic field 
and watch how it moves. There is no isolated pole, like an electric 
charge. Poles always come in paris, north and south together, they 
cancel out in the field and don't move under its force. 
    In thought experiment we place a north pole in the field and trace 
out its trajectory. This is the magnetic line of force. Arrows along 
it in diagrams show the motion of the test pole. 

Gauss's Law for charge 
 --------------------
    Imagine a spherical shell enclosing some electric charges, a mix 
of positive and negative ones. They may be scattered inside the shell, 
not bunched at the center. For simplicity, each charge has the same 
strength and is assigned one line of force. 
    The force line from a positive charge aims outward. That from a 
negative charge points inward. These are the directions of motion of a 
positive test particle placed on the line.  
    All  lines of force pass thru the enclosing sphere, some inward, 
some outward. Tally the in and out lines, algebraicly, over the 
sphere.  Each inward line offsets a outward line, leaving leftover 
lines of one polarity. Toss the offfset pairs and keep the leftover 
lines. 
    Each pair of lines represents a positive-negative pair  of charges 
inside the sphere. Any left over lines, with no paired opposite ones, 
are attached to extra positive or negative charges in the shell. 
    Gauss's law for charges states that on an enclosing sphere with 
charges within it, the algebraic count of lines of force, the electric 
field, all over its surface equals the net electric charge within the 
sphere. Gauss worked this out in 1835 for both electric charges and 
magnetic poles. 
   Gauss's law itself can not tell the separate number of charges, 
only the residual unpaired ones. You could have 20 gazillion electrons 
and 20 gazillion and two protons. You 'see' only the two extra 
PROTONS. In words: 

    (electirc lines thru sphere) = (net charges inside sphere)

    The sphere does not have to be a sphere. It may be any shape so 
long as it is closed, ensuring that lines of force from inside must 
pass across its surface and not thru a rip, tear, other opening. It 
may have folds! A line passing thru one ply of a fold in one 
direction, passes an other ply in the opposite direction. Eventually 
it leaves the enclosure and is then counted. The spherical shape is 
routinely used  because of its simple geometry and maths. 

Gauss's Law for poles 
 -------------------
    Repeat the setup of the enclosing sphere with magnets inside. Let 
each north or south pole emit one line of force. The north pole lines 
point outward; south pole, inward. 
    Tally the lines passing the sphere. pair off the in and out lines 
and toss them and keep any left over unpaired lines. 
    Some north poles pair with south poles and their lines cancel in 
the tally. 
    We find that ALL lines papir with NO left over ones! No matter 
what mix of magnets are in the sphere, every un line is offset by an 
out line, leaving none as a net excess. 
    Gauss's law of poles  says that the net count of lines, the  
magnetic field, is always zero over the sphere. 
    The reason is that so far as we know there are no lone magnetic 
poles. EVERY pole has its mate of equal strength but opposite 
polarity. EVERY enclosing sphere contains EXACTLY equal numbers of 
north and south poles and the net magnetic field on the sphere is 
ZERO. 
    Like for Gauss's law for charges the separate number of poles 
inside the sphere is not determined. Only the excess of north or south 
poles can be found, which is always none. 
    This in words is: 

    (magnetic lines thru sphere) = (zero net poles inside sphere) 

Maxwell's Equations 
 -----------------
    In 1864 Maxwell issued his theory of electromagnetism, uniting the 
two separate disciplines into a new single construct, electromagnetic 
wave or radiation. He demonstrated that all of the phaenomena of 
electricity and magnetism can be reduced to four fundamental 
equations. They are elaborations of Gauss's law for charge, Gauss's 
law for poles, Faraday's law, Ampere's law.  
    Maxwell's equations in words are: 

 +----------------------------------------------------------------+ 
 |  MAXWELL'S FOUR EQUATIONS OF ELECTROMAGNETISM                  | 
 |                                                                | 
 | electric field on Gauss sphere = net electric charge in sphere | 
 |                                                                | 
 | magnetic field on Gauss sphere = zero magnetic poles in sphere | 
 |                                                                | 
 | changing magnetic field around wire -> elec current in wire    | 
 | electric current in wire -> magnetic field around wire         | 
 + ---------------------------------------------------------------+ 

   These equations divide into two groups. The Gauss equations relate 
to poles and charges at rest. They cover electrostatics and 
magnetostatics.They deal with each field separately without 
commingling them. 
    The Ampere and Faraday equations relate to charges in motion or 
magnetic fields in motion. They deal with electrodynamics and 
magnetodynamics. 

Gauss's Law for mass 
 ------------------
    We divert to examine an other Gauss sphere and  the field on it. 
This is sometimes left out of home astronomy dialog on cosmology but 
it is one of its most fundamental principles. 
    Same Gauss sphere with some particles of mass inside. Each 
particle has a single gravity line of force. Because gravity is an 
attracting force, a small test mass moves inward along the line.
    Tally the lines over the sphere, netting the inward oneS with 
outward ones. 
    We find that ALL lines are inward! There are no outward lines. 
    Gauss's law for mass  states that the count of lines, the gravity 
field, over the sphere is the TOTAL mass within the sphere. Not a net 
of 'positive' and 'negative' mass but ALL of it as only 'positive'. 
    Entirely unlike Gauss spheres for charges and poles, we can add  
only mass of the one kind and increase the count of lines on the 
sphere. There is no way to add mass that cancels out some lines, like 
 for charges, or all of the them, like for poles. 
    Cosmology is often a part of relativity. In such work gravity is 
the force that governs the behavior of the universe on the larger 
scales of volume. 
    There are vast magnetic and electric fields in space. They are 
crucial for the study of nebulae, stars, galaxies. Astrophysicists 
need a solid grounding in electromagnetic theory. 
    look again at the three Gauss's laws. On the scale of many 
millions of lightyears, like within a galaxy cluster, there are inside 
a Gauss sphere immense numbers of charges, poles, particles. 
    Because every magnetic pole has a matching opposite pole, there is 
no imbalance of poles inside the sphere. 
 no net magnetic poles. The force lines thru the sphere cancel to 
zero. Altho locally, within stars or nebulae, magnetic forces are 
important, on the grand universal scale they are absent. 
    There are individual charges, such as electrons and protons, in 
space. Within stars and nebulae we have humongouss flows of protons or 
electrons separate from each other. A Gauss shell around these local 
volumes can contain an unbalanced number of charge. 
    On the larger scale it is excedingly tough to sustain charge 
segregation. The forces between opposite charges is incredibly strong, 
overcoming other natural forces that try to keep the charges apart. A 
Gauss sphere tends to enclose less and less imbalance of charge, more 
and more equal numbers of positive and negative charges. The electric 
field and its force tend to zero. 
    Looking at enclosed mass we have a whole different situation. 
There being only one kind of mass, a Gauss sphere of ANY size will 
contain an imbalance of mass, all 'positive'. 
    The larger the sphere the more mass it embraces as the sphere 
ropes in ever larger volumes of space. The gravity field on its 
surface also increases, this being the ever greater count of gravity 
lines of force from  the interior atoms. 
    On the scale of the whole universe the only governing force is 
gravity. Cosmology is truly driven by the action of the mass, and not 
the poles and charge, within the universe. 

Maxwell's waves 
 --  ---------
    When Maxwell studied the four cardinal formulae, he found that 
they are properties of single new entity, a wave of perpendicular 
interacting electric and magnetic fields. We examine some major 
features of this new wave. 
    A general wave function, such as a mechanical wave,, looks like 

    d^2(amplitude) / dx^2 = (dt^2 / dx^2) * (d^2(amplitude) / dt^2) 

    The amplitude of the wave is the displacement of the wave 
perpendicular to the  direction of the wave's motion. It is a math 
expression, like a sine function. 
    The 'd's are part of the symbols for 'derivative' in calculus, 
which we won't actually handle as such. 
     The left side relates amplitude to the downrange place along the 
direction of wave motion, or the  x-axis. The right side relates 
amplitude to the time elapsed since the wave started from the zero 
point of the x-axis. 
    In his investigations of the interaction of electric and magnetic 
fields Maxwell developed an expression for the strength of the 
electric field 

    d^2(strength) / dx^2  = mu * epsilon * d^2(strength) / dt^2) 

    He compared this with the general wave equation and matched the terms. 
The amplitude in the general case becomes  the electric field 
strength. 
    The dt^2/dx^2 becomes (mu*epsilon). These two parameters are the 
ability of the medium, in which the wave travels, for sustaining a 
magnetic (for mu)  or electric (for epsilon) field. 
    Some substances let a magnetic field penetrate them well while 
others are good shields against the field. This permeability of the 
medium is expressed by mu. 
    A similar reasoning applies to an electric field. epsilon is the 
permittivity of the medium. 
    Before Maxwell, these parameters were experimentally measured for 
a huge assortment of materials as basic properties of these materials. 
    When the material was a vacuum the mu and epsilon are denoted 
epsilon0 and mu0 is used. 

mu0 and epsilon0 
 --------------
    The Maxwell's wave formula we see the matching of terms and 
letting the medium be a vacuum. 

    dt^2 / dx^2 = epsilon0 * mu0 
                = (dt / dx)^2 
                = 1 / speed^2 

    speed^2 = 1 / (epsilon0 * mu0) 

    speed = sqrt(1 / (epsilon0 * mu0)) 

     When Maxwell plugged in the a;ready known values for mu0 and 
epsilon0 he came up with a speed of his electromagnetic waves. It 
matched virtually exactly the a;ready known speed of light! 
   From his other work with electromagnetic waves, he already 
explained optical effects, including refraction of light across media. 
    In 1876 Maxwell revealed that light was not a distinct phaenomenon 
in nature. Light was an electromagnetic wave behaving according to his 
theory. 
    we have here three basic parameters, all historicly determined by 
experiment by three different schools of physics. The speed of light 
was mechanicly measured by physicists dealing with light. 
    mu0, the permeability of a vacuum, was measured by scientists 
working with magnets. 
    epsilon0, the permittivity of a vacuum, was measured by scientists 
in the electricity discipline. 
    The values of all three were published in the physics litterature. 
    Values for epsilon0 and mu0 are now  folded into the metric system 
of measures as 

 +----------------------------------------------+ 
 | ELECTROMAGNETIC CONSTANTS                    | 
 |                                              | 
 | c = 2.998e8 meter/second                     | 
 |                                              | 
 | mu0 = 4*pi*1e-7 newton/ampere2               | 
 |     = 12.567e-7 newton/ampere2               | 

 |                                              | 
 | epsilon0 = 8.854e-12 coulomb2/newton.meter2 | 
 +----------------------------------------------+  

Where's the medium?
 -----------------In Maxwell's time light was believed to travel thru 
a physical medium, like other waves then known. altho a vacuum 
contained nothing, it just had to be filled with a substance, the 
aether, that conveyed light thru outer space. c, the speed of light in 
vacuum, was the speed of light thru this aether. 
    Attempts to detect the aether were tried in the 1880s. The first 
was the Michelson-Morley experiment to measure the speed of light at 
various directions from the Earth's orital  motion. 
   The thinking was the light would travel faster or slower as Earth 
moved into or away from a beam of light, like a boat's speed is found 
by tracking a floating object thrown forward and then rearward. 
    All attempts failed to yield changes in c with orientation. c was 
the same with one nasty interpretation being that Earth did not move, 
but in fact stood still in space. 
    We don't take up relativity here but we can appreciate how 
lightspeed can be a constant for every one. It comes from two physical 
properties of nature, epsilon0 and mu0. c is an algebraic combination 
of these parameters, tehmselfs constants. The properties of a vacuum 
don't change with motion of the observer. 
    Physicists wrestled with this situation with many curious 
explanations. In 1905 Einstein showed that light did not need an 
actual medium and c was the same for all observers. From this 
realization he developed the theory of special relativity.

Refraction of Light 
 -----------------
   Maxwell found that he could explain all the phaenomena of light 
which were previously known only thru experiment and empirical rules. 
For rxample, Snellius in 1621 figured the law of refraction. Until 
thrn trgtavtion wwas a tabulated function.  Ptolemaeus in about 130 AD 
first compiled tables of refraction. Ptolemaeus, lacking good 
instruments and trigonometry, could not come up with a proper 
analysis.
    Snellius's law is 

 n1 * sin(a1) = n2 * sin(a2) 

    a1 is the angle of the light from medium 1 into medium 2. a2 is 
the angle of the light in medium 2. Both are measured from the 
orthogonal on the boundary of the media at the entry. point. 
    n1 and n2 are empiricly determined properties of medium 1 and 
medium 2, the index of refraction. It expresses the 'strength' of a 
medium for bending the path of light thru it. A larger index implies 
that light is more steeply bent than a medium with a smaller index. 
    The index is a relative one, banking off of a base medium as 
unity. For most earthly work, the base medium is air, with n - 1.000. 
For optics nuilt for use in  outer space, the vacuum is the medium as 
1.000 and air is a bit more. 
    The refraction index varies with wavelength, which makes possible 
prism spectrometers, but here we ignore this feature. 
    In the diagram here the boundary between the two media is the 
vertical line '#'. The horizontal line is the perpendicular at the 
entry point of the light ray. The ray comes from the left in medium 1, 
index n1, at an angle of incidence a1. It enters medium 2, index n2. 
    It continues in medium 2 with angle of refraction a2,. 


                     #       /      
                (n1) #     / ) 
                     # /   a2  ) 
          - - - - - -#- - - - - - - -
             (  a1  /#  
               (  /  #  (n2) 
                /    # 

    Maxwell thru his EMW theory worked out that refraction across two 
media is 

    sqrt(1 / (mu1*epsilon1))) * sin(a1) = 
               
which is the same form as the empirical Snellius law. Matching terms 
from Snellius and Maxwell, we see that 

    sqrt(1 / (mu1*epsilon1))) = n1

    sqrt(1 / (mu2 * epsilon2)) = n2 

    From the wave equation 

   sqrt(1 / (mu1*epsilon1)) = speed1 

   sqrt(1 / (mu2*epsilon2)) = speed2 

These are the velocities of light in each medium. 

    speed1 * sin(a1) = speed2 * sin(a2) 

    Because medium 1 is prevalently vacuum or air, speed1 is c itself. 

    c * sin(a1) = speed2 * sin(a2) 

    c / speed2 = sin(a2) / sin(a1) 

    speed2 / c = n1 / n2 
               = 1.000 / n2 
              -> 1 / n2 
 
    The indices of refraction are the ratios of the speed of light in 
vacuum (or air) to that in medium2. n1 for air or vacuum is set to 
unity, so the ratio is always 1/n2. 
    The sense is that in a medium other than a vacuum light travels 
SLOWER than c. 

    Maxwell by this analysis showed that refraction index is a direct 
feature of electromagnetic waves. And it applies to EMW of any 
wavelength, not just those exciting vision. 

Cherenkov effect 
 -------------- 
    The diminished speed of light within media other than a vacuum 
leads to a peculiar effect described by Cherenkov in about 1950. In 
nuclear experiments particles are accelerated to very nearly the 
lightspeed. When they are sent into a detection medium, such as liquid 
helium, they emit light in a pattern resembling the wake of a boat in 
water! The light LAGS the particle and is left behind! The nuclear 
particle is moving faster than light! This is the Cherenkov effect. 
    The particle is moving faster than the REDUCED lightspeed within 
the helium. The light radiates away at the actual speed of light for 
that medium and slower than particle itself. 
    No Einstein rules are broken. It remains true that no matter can 
excede the speed of light in vacuo, but it is also true that it can 
excede the slower speed of light within the medium it passes thru. 

Propogation of EMW
 ----------------
    Altho Maxwell's theory explained optics and radiation with 
electromagnetic eaves, these waves were only a maths model. Was light 
the only electromagnetic wave? Can other kinds exist? Can we 
deliberately make an electromagnetic wave? 
    Hertz in 1886 was the first to generate artificial  
electromagnetic waves. He built an electric circuit that oscillated 
electric and magnetic fields. he rigged up an other circuit to 
receive them. This was the birth of the electromagnetic industry. 
    Today we produce RMW by electronic devices, like at broadcast 
transmitters. They produce oscillating electric and magnetic fields 
which are released into the air as EMW thru an antenna. In the sketch 
    here '#' is the transmission house, '=' is the antenna. 

    ++  A  --         <- B <-         --  C  ++         -> D -> 
    +===#-==-         ===#===         -===#===+         ===#=== 
     >>>>>>>          .......          <<<<<<<          xxxxxxx 
                         >>>>>        ........          <<<<<<< 
                                       >>>>>>>          .......  
                                                        >>>>>>> 

    Scene A has the base oscillator sending electrons to the right end 
of the antenna and sucking them out of the left end. The positive 
charge there comes from the atomic protons that no longer have 
electrons to offset them. The separated charges produce an electric 
field pointing right, '>'. 
    Scene B has the base 1/4 oscillation cycle later when it stops 
pumping electrons. The electrons at right end of the antenna racing 
left. '<-'. This current sets up a magnetic field pointing out, to 
you, '.' suggesting an arrow point. It pushes away, sown in the 
sketch, the electric field from the previous 1/4 cycle. 
    Scene C is at the 2/4, 1/2, cycle when the base pumps electrons 
from the right end. This separated charge yields an electric field 
pointing left , '<'. It pushes the previous electric and magnetic 
fields away. 
    Scene D is at 3/4 cycle of the oscillator. Pumping stops and 
electrons race right along the antenna, '->'. They generate a magnetic 
field pointing away from you, 'x', alluding to arrow feathers. This 
field shoves away the earlier electric and magnetic fields. 
     After scene D the transmitter circuit begins a second cycle back 
at scene A. The fields travel away at lightspeed to constitute the 
electromagnetic wave. 
    We now stand downrnge from the broadcast base and watch the wave 
pass by. The base sends out in alternation an electric and then a 
magnetic field in  a sequence of repeating cycles. The fields are 1/4 
1/4 cycle out of step. As one is cresting to its maximum strength the 
other is passing thru its zero strength. 
    Stand alongside an EMW passing in front of us, we see something 
like this, where the wave is traveling to the right along the x-axis 
at speed c.
     This is a snapshot of several wavelengths of the EMW showing the 
direction of the two interacting fields. The base is off-page at the 
left and wave travels by us left to right. Prior segments move to the 
right farther downrange. 

  ^^^ ... vvv xxx ^^^ ... vvv xxx ^^^ ... vvv xxx ^^^ ... vvv xxx 
  ^^^ ... vvv xxx ^^^ ... vvv xxx ^^^ ... vvv xxx ^^^ ... vvv xxx 
  ^^^ ... vvv xxx ^^^ ... vvv xxx ^^^ ... vvv xxx ^^^ ... vvv xxx 
           |               |           |               | 
           |<-wavelength-->|           |<-wavelength-->| 

    ^ = positive pointing electric field (arrow up) 
    . = north pointing magnetic field  (arrow point) 
    v = negative pointing electric field (arrow down) 
    x = south pointing magnetic field (arrow feathers) 

    The distance between corresponding points on successive cycles is 
the wavelength of the EMW. This distance is NOT only that between 
peaks or zero points of successive waves, as some books assert.
    The number of wavelengths passing by us per second, traveling at 
speed c, is the frequency of the wave. We ,au designate this wave by 
wither its wavelength or frequency according as local practice. 
     For waves sent out by AM radio stations, the frequency is in 
hundreds of kilohertz. In the FM band it's tens of megahertz 
     By standing within the wave and facing into it, we experience a 
cyclical succession of electric and magnetic fields, shown here in 
steps of 1/4 cycle.  

   ^^^  <<<  vvv  >>>  ^^^  <<<  vvv  >>>  ^^^  <<<  vvv  >>> 
   ^^^  <<<  vvv  >>>  ^^^  <<<  vvv  >>>  ^^^  <<<  vvv  >>> 
   ^^^  <<<  vvv  >>>  ^^^  <<<  vvv  >>>  ^^^  <<<  vvv  >>> 
    0    1    2    3    4    5    6    7    8    9   10   11 

         |<----one cycle---->|    |<----one cycle---->| 

    ^ = positive pointing electric field (arrow up) 
    < = north pointing magnetic field (arrow left) 
    v = negative pointing electric field (arrow down) 
    > = south pointing magnetic field (arrow right)
    0, 1, 2, ... = successive quarter cycle interval. 

Energy of a Field 
 ----------------
    An electric field carries energy coming from the energy spent to 
create the field.. Without going thru the derivation, we note that 
given a field of strength E, the density of energy, joule/meter3, is 

    densityE = (epsilon0 * E^2) / 2 

where E is the electric field strength 
    A parallel formula gives the energy density of a magnetic field 

     densityB = ((1(1 / mu0) * B^2) / 2 

also in joule/meter3.  
    The electric field strength is measured in newton/coulomb, parallel 
to the gravity field strength in newton/kilogram. 
    The magnetic field strength is in (newton.second)/(coulomb.meter) 
or newton/(ampere.meter). Recall that coulomb/second = ampere. This 
odd unit comes from the way we define magnetic field strength by way 
of an electric current. 

Energy in EMW 
 -----------
    As an EMW passes over an observer he sees the electric and 
magnetic fields in alternation. The energy densities of these fields 
are added together to give the total energy density of the EMW. 
    The two fields alternate in cresting and zeroing. The energy 
producing the fields is exchanged between them as each field rises and 
falls in strength during a cycle. The sum of the two portions is 
constant, equal to the input energy of the generator.  We have 
    We have for an electromagnetic wave 

     densityEMW = densityE + densityB 
            = ((epsilon0 * E^2) / 2) + (((1 / (mu0) * B^2) / 2) 

           = (((epsilon0 * E^2) + ((1 / mu0 ) * B^2)) / 2 

    This does not mean the two individual densities are always the 
same. Each varies as the amplitude of its field, 1/4 cycle offset from 
te other field. The SUM of the two is constant over the entire cycle. 
    Also this equation deals with the energy content of the fields, 
NOT strengths. The two fields have entirely different field strengths 
and their sum over a cycle is not constant. 

Root Mean Square 
 --------------
    The energy equations are based on the instantaneous strengths of 
the electric and magnetic fields. In an EMW the two fields vary in 
strength from a maximum positive value to a maximum negative value in 
a given cycle. It is normally not practical or important to measure 
the fields at a given instant and work out the energy densities. 
    If the wave has any considerable frequency, the oscillation of 
fields is so rapid that it looks like a steady field of equivalent 
strength as the real one. For most motors, heating, lighting, 
household  applications don't need a detailed profile of the wave. 
They can be built to accept an equivalent steady energy flow. 
    From long experience in engineering a fair and overall good 
equivalent wave energy density is sqrt(2)*(maximum). In decimals this 
is (0.707)*(maximum). For rough work you may use 0.7. This is the 
'root mean square', or 'RMS', field energy treated as tho it were a 
steady, not varying, field. We have 

    densityRMS = densityErms + densityBrms 
               = epsilon0 * Erms^2) / 2 + ((1 / mu0) * Brms^2) / 2 
        = ((epsilon0 * Erms^2) + ((1 / mu0) * Brms^2)) / 2 

    Just about all uses of EMW work with the RMS value of its energy 
density, often without actually stipulating it as such. If you really 
mean the peak value you have to deliberately say so. 
    By removing, for practical purposes, the varying values of 
electric and magnetic energy density, replacing them with the level 
RMS value, we have 

    densityRMS = densityErms + densityBrms
               = (epsilon0 * Erms^2) / 2 + ((1 / mu0) * Brms^2) / 2 
               = ((epsilon 0 *Erms^2) + (((1 / mu0) * Brms^2)) / 2 
               = ((epsilon0 * Erms^2) + (epsilon0 * Erms^2)) / 2 
            =*2 * epsilon0 * Erms^2 / 2
            = epsilon0 * Erms^2 

    We can simply add the two rms values and then equate them because 
the RMS value is a levelizing of the field variation into a steady 
uniform  field. 
 
 Electric Field Overwhelms 
 -----------------------
    Recall that the RNS electric and magnetic energy densities are 
equal, we have 

    (epsilon0 * E^2) / 2  = ((1 / mu0) * B^2) / 2 

    epsilon0 * E^2 = (1 / mu0) * B^2 

    epsilon0 * E^2 / B^2= 1 / mu0 

    E^2 / B^2 = 1 / (epsilon0 * mu0) 

      E / B = sqrt(1 / (epsilon0 * mu0)) 
            = c 
    This is an extraordinary result! The electric field strength is 
some 300 million times greater than the magnetic field strength in an 
electromagnetic wave.
    Any authors scramble this statement really good. The energy 
densities of the fields are the same in an EMW. The field strengths 
themselfs in that EMW are vastly different. 
    What this means is that we routinely depict in textbooks an EMW as 
a SINGLE field, the electric field, orthogonal to the direction of  
propagation. In optics, for instance, a lightwave is a single 
oscillating field, the electric field This one-field model  does help 
explain polarization easier than with the both fields. 
    To see how vastly larger the electric field strength is, make a 
scale drawing of an EMW with the two intersecting fields. Let the peak 
magnetic field strength be one millimeter. What is the height of the 
electric field strength on the same scale? E?M = 300 million and M = 
1mm, making E be, hold your hat, 300 KILOMETERS tall! You need a hell 
of a large paper for the drawing. 

Irradiation 
 --------- 
    When an electromagnetic wave is intercepted by a target it 
delivers its energy to the target. This energy can be wasted as heat 
or utilized to produce work. 'Work' is a very general term meaning any 
action useful to humans. One action crucial for astronomy is exciting 
the eye to produce vision. The eye pupil is the target. 
    As the EMW flows over the target, a certain volume of it passes 
thru the target per second. The energy within this volume is imparted 
to the target as  energy per unit time, or power. time. 
    The irradiation on the target is this energy/meter3  times the 
speed of the wave, which is c the speed of light. 

    irradiation = densityEMW * c 

    Irradiation is in joule/meter2.second, or watt/meter2. The 
joule/second has the special name 'watt', the unit of energy flow, or 
power. The target has an area facing the EWMW in meter2. The total 
power captured is the irradiation times this area, 

    power = irradiation * area 

This power is converted by the target into work. In this way 
electromagnetic waves allow us to accomplish useful work from a remote  
station without wires. 

Sun's irradiation 
 ---------------
     the Sun's irradiation is nearly enough 1,350 watt/meter2. This is 
from satellite observations at the Earth's distance from the Sun. It 
varies with Sun distance from Earth, sunspot cycle, solar eruptions, 
secular changes. It is attenuated by the atmosphere to around 1,3200 
W/m2 at the ground. 
     What is the strength of the Sun's electric field? 
    The energy density of the EMW is the irradiation divided by speed 
of light 

    densityEMW = irradiation / c 
               = (1,350 W/m2) / (2.988e8 m/s) 
               = 4.518e-6 W.s/m3 
               = 4.518e-6 J/m3 

The electric field strength is 

    densityEMW = epsilon0 * E^2 
    
    E^2 = densityEMW / epsilon0 
        = (4.518e-6 J/m3) / (8.854e-12 C2/N.m2) 
        = 5.103e5 J.N.m2/m3.C2 
        = 5.103e5 N.m.N.m2/m3.C2 
        = 5.103e5 N2.m3/m3.C^2 
        = 5.103e5 N2/C2 

    E = sqrt(5.103e5 N2/C^2) 
      = 7.144e2 N/C 
     -> 714 newton/coulomb 

    A more familiar statement is, with the definition of the 'volt' as 
one joule/coulomb is 

    newton/coulomb = newton.meter/coulomb.meter 
                = joule/coulomb.meter 
                = volt/meter 

    The energy density of the  electromagnetic radiation is in 
joule/meter3. One joule m the unit of energy or work,is itself one 
newton.meter. We have 

    joule/meter^3 = newton.meter/meter^3 
                  = newton/meter^2 

which is a force over a unit area, or pressure. 
    An incident EMW of a given energy density exerts on a target 
surface a pressure equal in value to that energy density. 
    If we have the irradiation of the wave, in watt/meter
    for the Sun at Earth distance away the radiation pressure is 

    pressureEMWW = densityEMW
                 = 4.685e-6 N/m2 

    +-----------------------------------+ 
    | IRRADIATION PARAMETERS OF SUN      | 
    |                                    | 
    | irradiation = 1.350 W/m2           | 
    |                                    | 
    | elec field strength = 7.144e2 N/C  | 
    |                                    | 
    | energy density = 4.518e-6 J/m3     | 
    |                                    | 
    | radiation pressure = 4.5185e-6 N/m2 | 
    +------------------------------------+ -