__Part One:__The Basics of Electrodynamics & How It Relates to PEMF DevicesIntroduction The Electromagnetism- Forces, Energy, & Waves

**I. Electrostatics - Charges at Rest (Electric Charge, Coulombs Law & Gauss's Law)**

II. Charges in Motion Part 1 (Voltage, Capacitance & Basic Circuits)

III - Introduction to Magnetism, Magnetic Forces and Magnetic Fields

IV. Magnetism Part 2 - Lorenz Force Law, Biot Savart Law, Ampere's Law & The Really Big Lie in PEMF (Most Important Video in Physics Review Series)!!

V. Faraday's Law of Induction & Applications to PEMF Therapy

__Part Two:__The Physics of Energy TransferVI. - Electric Power and Transformers- Electric Energy Transfer and Inductive Energy Transfer.

VIII. Maxwell's Equations - Bringing it ALL Together

IX. Solving Maxwell's Equation for Free Space (Homogeneous Solutions) - LIGHT

X. Solving Maxwell's Equations Most General Solution (Inhomogeneous solutions) - Velocity and Acceleration fields (bound and free fields). Now we can talk about the different types of energy medicine devices and make CLEAR distinctions.

XI. Resonance - Mechanical, Electromagnetic and Wireless Power Transmission

XII. Magnetic Resonance Stimulation - The Choral Fantasy

Let us Start with Electricity and Electric Charge:

**I. Electrostatics - Charges at Rest (Electric Charge, Coulombs Law & Gauss's Law)**

**Electromagnetism (Electricity, Magnetism and Electromagnetic Waves)**

To Understand Electromagnetic Waves and PEMF Therapy, it is important to understand Electricity and Magnetism.

Most of you have a direct experience with electric charge. Really try to get an intuitive understanding of charge because EVERYTHING in electromagnetism (light included) comes from static, moving or accelerating charges.

**I. Electrostatics - Charges at Rest**

Force of Electrostatics...

Force of Electrostatics...

Perhaps you have walked across a carpet on a dry day and reached out your hand to touch door knob and received a small shock, or when separating your bed covers at night you've heard a crackle and seen the light glowing under from under you covers as you pull them off. Electricity is the property of some particles of matter related to electric charge.

From ancient times, people were familiar with different types of phenomena that today would all be explained using the concept of electric charge:

(a) lightning,

(b) the torpedo fish (or electric ray),

(c) St Elmo's Fire, and

(d) that amber rubbed with fur would attract small, light objects.

It has been recorded that Thales of Miletus around 640 B.C. rubbed amber (which is fossilized tree sap) and discovered it would attract leaves.

THAY:leez of mi:LAY:tus

In fact the word electron comes from the Greek or Latin word for Amber.

(a) lightning,

(b) the torpedo fish (or electric ray),

(c) St Elmo's Fire, and

(d) that amber rubbed with fur would attract small, light objects.

It has been recorded that Thales of Miletus around 640 B.C. rubbed amber (which is fossilized tree sap) and discovered it would attract leaves.

THAY:leez of mi:LAY:tus

In fact the word electron comes from the Greek or Latin word for Amber.

Today we know that electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

There are two types of electric charges; positive and negative (commonly carried by protons and electrons respectively).

Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral.

By some strange convention, electrons were given this minus sign by Benjamin Franklin.

The first interesting thing is that every electron anywhere in the universe has exactly the same charge. It also has exactly the same mass. But at the microscopic level of electrons and protons, every electron and every proton anywhere in the universe is identical. I find that fascinating.

Secondly charge is conserved. Conserved is a physics terms for saying — does not change with time or charge cannot be created or destroyed.

Thirdly, Charge is quantized (that is charge is granular not continuous); it comes in integer multiples of individual small units called the elementary charge, e, about 1.602×10−19 coulombs, which is the smallest charge which can exist free (particles called quarks have smaller charges, multiples of 1/3 e, but they are only found in combination, and always combine to form particles with integer charge). The proton has a charge of +e, and the electron has a charge of −e.

Interestingly even though protons weight approximately 1800x electrons, their charges are identical.

Here is a little experiment you can do to illustrate the Electrostatic Force that is illustrated in this short video clip.

Take a plastic comb and some little pieces of paper.

Comb your hair nice and good and then hold the comb over the paper.

The paper "Jumps" up to the comb if the comb is a reasonable distance away.

Now that might seem like no big deal, BUT, the electrostatic force of electrons on a little comb TRIUMPHS over the gravitational force of the ENTIRE MASS OF THE EARTH!!!!

The reason for this is the electromagnetic force is more than a trillion trillion trillion 10^36 times stronger than gravity. The reason Gravity WINS cosmically on the large scale is because most things are electrically neutral.

Yes. Most things are electrically neutral. In other words, electric force, even though it’s very strong, comes with opposite charges. It can occur with a plus sign or with a minus sign. Therefore, if you take the planet Earth, it’s got lots and lots of charges in every atom, but every atom is neutral.

There are two types of electric charges; positive and negative (commonly carried by protons and electrons respectively).

Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral.

By some strange convention, electrons were given this minus sign by Benjamin Franklin.

The first interesting thing is that every electron anywhere in the universe has exactly the same charge. It also has exactly the same mass. But at the microscopic level of electrons and protons, every electron and every proton anywhere in the universe is identical. I find that fascinating.

Secondly charge is conserved. Conserved is a physics terms for saying — does not change with time or charge cannot be created or destroyed.

Thirdly, Charge is quantized (that is charge is granular not continuous); it comes in integer multiples of individual small units called the elementary charge, e, about 1.602×10−19 coulombs, which is the smallest charge which can exist free (particles called quarks have smaller charges, multiples of 1/3 e, but they are only found in combination, and always combine to form particles with integer charge). The proton has a charge of +e, and the electron has a charge of −e.

Interestingly even though protons weight approximately 1800x electrons, their charges are identical.

**Electrostatic Force**Here is a little experiment you can do to illustrate the Electrostatic Force that is illustrated in this short video clip.

Take a plastic comb and some little pieces of paper.

Comb your hair nice and good and then hold the comb over the paper.

The paper "Jumps" up to the comb if the comb is a reasonable distance away.

Now that might seem like no big deal, BUT, the electrostatic force of electrons on a little comb TRIUMPHS over the gravitational force of the ENTIRE MASS OF THE EARTH!!!!

The reason for this is the electromagnetic force is more than a trillion trillion trillion 10^36 times stronger than gravity. The reason Gravity WINS cosmically on the large scale is because most things are electrically neutral.

Yes. Most things are electrically neutral. In other words, electric force, even though it’s very strong, comes with opposite charges. It can occur with a plus sign or with a minus sign. Therefore, if you take the planet Earth, it’s got lots and lots of charges in every atom, but every atom is neutral.

Coulomb's law is an exact formula derived from experiment that allows us to calculate the Electrostatic Force between 2 or more charged particles (superposition).

The force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The constant of proportionality k = 1/4pi*eo.

eo is the electric permittivity constant in free space and is a measure of how much a vacuum in space shields the electric charge (we'll come back to this later and ultimately see how it is tied to the speed of light!).

It looks a lot like the gravitational force between two point masses except the we multiply charge instead of mass and the constant is different. But they are both inverse square laws.

It is actually much more practical to work with the field formulation using the electric field. The reason is that whereas q1 and q2 exist only at these two places,

The force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The constant of proportionality k = 1/4pi*eo.

eo is the electric permittivity constant in free space and is a measure of how much a vacuum in space shields the electric charge (we'll come back to this later and ultimately see how it is tied to the speed of light!).

It looks a lot like the gravitational force between two point masses except the we multiply charge instead of mass and the constant is different. But they are both inverse square laws.

It is actually much more practical to work with the field formulation using the electric field. The reason is that whereas q1 and q2 exist only at these two places,

**the electric field can be defined everywhere as we'll see**.**Electric Field**

Define F = qE

E = F/q

E is called the electric field of the source charge(s). Notice it is a function of position because the separation "r" depends on the location of the field point.

What exactly is an Electric Field?

James Clerk Maxwell identified the field as the space around an electrified object - a space where electric forces act.

Each electric charge produces in its vicinity an electric field that exerts a force on other charges (just like the smell of a skunk repels or perhaps attracts other animals). Field is like sound of one hand clapping. You don't need 2 charges, just one.

Field formulation does away with action at a distance and is very powerful in ALL areas of physics, where forces are mediated by the field (the FIELD produces the force).

The common thread running through most attempts to define the electric field is that fields and forces are closely related. Here's a pragmatic definition: An electric field is the electrical force per unit charge exerted on a charged object.

Although philosophers debate the true meaning of the electric field, practical problems can be solved thinking of the electric field at any location as the Number of newtons of electrical force exerted on each coulomb of charge at that location.

E = F/q

The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, and by time-varying magnetic fields.

So really all we are doing is taking Coulombs law and dividing by q. What this gives us is the FIELD around ONE (or more by superposition) source charges. That way it defines all of space no matter where we place the other "test charge".

It is helpful to visualize the electric field in the vicinity of a charged object.

Try to get used to this field formulation because we'll be using it in electric fields, magnetic fields and even LIGHT! Iron fillings around a bar magnet is probably the easiest example to visualize and it is much like that with electric fields too.

**Visualizing Force Fields Around Charges - Electric Field**

You can draw the Electric field vector at each point and join the vectors. When you join the lines you lose information on magnitude of field.

Due to the miraculous property of the coulomb force, namely that it falls like 1 over r^2, there is information even on the strength of the electric field, and that information is contained in the density of electric field lines.

By density of lines, I mean the number of lines crossing a surface perpendicular to the lines, divided by the area of that surface.

To understand Electric Field Flux (which we are going to talk about next), try to see this field lines as a FLOW of the electric field out from a positive charge (like a faucet flowing water out), and a Flow of electric field INTO a negative charge, like a drain. Fluid flow and flux is mathematically isomorphic (same form) to electric field flow/flux.

**Gravitational Force is similar except because of inertia of mass gravitational FIELD is proportional to gravitational force (no need to divide by mass like you have to divide by charge). The deep reason for this is that gravity is the curvature of spacetime and the gravitational field is a geometrical.

**Example of Electric Fields around points, lines, sheets and spheres**

Notice even though the Electric Field is a 1/r^2 equation, it is ONLY SO for point charges and spheres of charge (we'll come back to this later magnetic fields as it is part of the BIG LIE with high intensity companies).

Notice even though the Electric Field is a 1/r^2 equation, it is ONLY SO for point charges and spheres of charge (we'll come back to this later magnetic fields as it is part of the BIG LIE with high intensity companies).

**Gauss's Law & the Flux of a Vector Field**

Gauss's law for electric fields relates the spatial behavior of the electrostatic field to the charge distribution that produces it. It gives the SAME result as Coulombs law, but it is more powerful and many times easier to use mathematically.

Simply put it states: Electric Charge produces an electric field, and the flux of that field passing through any closed surface is proportional to the total charge contained within that surface (divided by the permittivity).

Electric Flux Through a Closed Surface = Qinc/eo

The analogy of fluid flow is very helpful in understanding the meaning of "flux" of a vector field such as the electric field. You can think of the flux of a vector field over the surface as the amount of that field that "flows" out through the surface.

So a spherical source would be a like a point source of water spraying at a constant rate out in all directions. If you put a spherical transparent balloon around that point source the total amount of water hitting the surface of the balloon is constant regardless of how big you make the balloon. Try to visualize that.

The flux has to stay constant because the amount of water flow is constant, so a small spherical surface will seem like a large pressure or force but the area is really small. A larger sphere will have less pressure per unit area, but the overall area is much larger.

The point is there is still the same amount of water flowing out. This is because water is ONLY flowing from the point source, otherwise water would have to material out of thin area or vanish to increase or decrease the flux.

LARGE PRESSURE/FORCE*small area = small pressure/force*LARGE AREA

So a spherical source would be a like a point source of water spraying at a constant rate out in all directions. If you put a spherical transparent balloon around that point source the total amount of water hitting the surface of the balloon is constant regardless of how big you make the balloon. Try to visualize that.

The flux has to stay constant because the amount of water flow is constant, so a small spherical surface will seem like a large pressure or force but the area is really small. A larger sphere will have less pressure per unit area, but the overall area is much larger.

The point is there is still the same amount of water flowing out. This is because water is ONLY flowing from the point source, otherwise water would have to material out of thin area or vanish to increase or decrease the flux.

LARGE PRESSURE/FORCE*small area = small pressure/force*LARGE AREA

E (the electric field) in Gauss's law represents the total electric field at each point on the (hopefully) symmetric surface under consideration. In our analogy Electric field is like the water pressure at a given spot on the surface. So in this case an point (or small area) on the smaller sphere has a more pressure or force than a point (or small area) on the larger sphere. Think about it... water pressure will decrease with distance from source, BUT overall water flow is constant. But the electric field is technically the force per unit charge but the idea is similar to fluid flow which is easier to visualize.

Symmetric in our examples will mean spherical/point, cylindrical/line or planar. If the surfaces are not symmetric we need to use Coulombs Law or more advanced mathematical techniques. But the basic principle is easily conveyed with symmetric objects.

Certain Problems that are highly symmetric you can get with Gauss's Law.

Symmetric in our examples will mean spherical/point, cylindrical/line or planar. If the surfaces are not symmetric we need to use Coulombs Law or more advanced mathematical techniques. But the basic principle is easily conveyed with symmetric objects.

Certain Problems that are highly symmetric you can get with Gauss's Law.

**Example point charge or sphere:**Take the field of a point charge q and compute its surface area on a sphere centered on it. The answer is q/eo independent of the radius of the sphere because the area of the sphere increases by r^2 while the field decreased by 1/r^2 so the flux remains the same. Isn't that amazing!! The 1/r^2 law is mostly geometric based on point charges or source spheres!!Notice in these examples ONLY spherical symmetry leads to an inverse square law. This is true with ALL inverse square forces. Lines, planes, rings and other source geometries DO NOT fall off by 1/r^2.

This becomes clear when we DO NOT see a 1/r^2 with charge/current lines, loops, planes and other geometries. That is because we have to integrate over the whole surface the electric field at each point on that surface.

For example, electric field drops off from a long wire of charge by 1/r and the electric field stays the same over a large plane of charge (no dropoff - thing about it, the higher above an infinite plane of charge you go, the MORE charges come into your view... you cannot escape an infinite plane of charge).

Gauss's Law gives the SAME result as Coulombs law for an electric field, BUT it greatly simplifies the equations when there is symmetry, like in spheres, cylinders, sheets of charge, lines of charge, etc. But if this is too confusing, just understand it is giving the same result as Coulombs law of the Electric Field around a charge source ANY distance away.

Some Cases Like a

This becomes clear when we DO NOT see a 1/r^2 with charge/current lines, loops, planes and other geometries. That is because we have to integrate over the whole surface the electric field at each point on that surface.

For example, electric field drops off from a long wire of charge by 1/r and the electric field stays the same over a large plane of charge (no dropoff - thing about it, the higher above an infinite plane of charge you go, the MORE charges come into your view... you cannot escape an infinite plane of charge).

Gauss's Law gives the SAME result as Coulombs law for an electric field, BUT it greatly simplifies the equations when there is symmetry, like in spheres, cylinders, sheets of charge, lines of charge, etc. But if this is too confusing, just understand it is giving the same result as Coulombs law of the Electric Field around a charge source ANY distance away.

Some Cases Like a

**Circular Loop of Charge**are Symmetric But It is Easier to Just Calculate the Electric Field By Brute Force. The reason this is important is that PEMF devices use circular current loops. This will become obvious later on. This helps us to EXPOSE the BIG LIE many High Intensity PEMF companies and so called experts say that PEMF fields drop off by 1/r^2... That is simply BAD BAD Science!!