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**Physics Review For Better Understanding PEMF Therapy and Energy Medicine**

"The Force is what gives the Jedi his power. It's an energy field created by all living things. It surrounds us and penetrates us; it binds the galaxy together."

--Ben Obi Wan-Kenobi (Star Wars)

The FORCE is LIFE FORCE, or life energy, also called chi, ki, prana, etc by ancient traditions. Life Force creates, animates, invigorates, sustains, supports, heals and nourishes your body and gives it energy. But the source of the bodys' energy at the physical and cellular level is primarily electromagnetic force in the high energy bonds of ATP and the voltage of the transmembrane potential.

PEMF at its most fundamental level boosts your energy and life force.

To understand the Basic Science of PEMF and expose the Bad science running rampant in the PEMF community, we need a solid understanding (for starters in Classical Electrodynamics). This is a good enough approximation without getting into the extremely complex mathematics of relativistic electrodynamics and QED, quantum electrodynamics. Understanding the Electromagnetic force begins with understanding what Force is.

--Ben Obi Wan-Kenobi (Star Wars)

The FORCE is LIFE FORCE, or life energy, also called chi, ki, prana, etc by ancient traditions. Life Force creates, animates, invigorates, sustains, supports, heals and nourishes your body and gives it energy. But the source of the bodys' energy at the physical and cellular level is primarily electromagnetic force in the high energy bonds of ATP and the voltage of the transmembrane potential.

PEMF at its most fundamental level boosts your energy and life force.

To understand the Basic Science of PEMF and expose the Bad science running rampant in the PEMF community, we need a solid understanding (for starters in Classical Electrodynamics). This is a good enough approximation without getting into the extremely complex mathematics of relativistic electrodynamics and QED, quantum electrodynamics. Understanding the Electromagnetic force begins with understanding what Force is.

**Force**: The influence that an object exerts on another object causing some change is FORCE. Where there is change, there is some kind of force behind it. Motion of an object (esp. acceleration) is an example of change.

**Interaction:**A mutual force between two objects through which they influence each other is an interaction. For example, two particles attract or repel each other due to attractive or repellent forces.

**There are 4 known Forces or interactions: Gravitational Force, Electromagnetic Force, Strong Nuclear Force and Weak nuclear force.**

Note Forces can be a result of direct contact (Applied, Spring, Friction, Drag, Tension, etc) OR by Force Fields (Gravity, Electromagnetic Forces, etc.).

Where there is Force there is energy, and the measure of the ability of a force to do work is energy. There are different kinds of energy corresponding to the different forces. All of these energies have the same UNITS (typically Joules). The flow of energy, that is energy transfer, is a key to maintaining order in the Universe, and in our bodys'. For example energy flows from the Sun to the plants, and from plants to our bodies in the form of food.

There are two main types of energy, kinetic energy which is energy of motion or movement and potential energy which is energy that is stored.

A force acting on a particle results in a change in the kinetic or potential energy of the particle. In energy medicine, we use different devices to move charges in the body with the overall goal of increasing energy and life-force.

Energy comes in different forms as shown in this chart. Most energy medicine devices are electromagnetic in Nature so we will focus on 3 main types of electromagnetic energy in this module. 1) Electrical Energy 2) Magnetic Energy 3) Light Energy. Though all are connected within the ONE electromagnetic force, they ARE all different in their properties and healing power (as we'll see in this course).

There are two main types of energy, kinetic energy which is energy of motion or movement and potential energy which is energy that is stored.

A force acting on a particle results in a change in the kinetic or potential energy of the particle. In energy medicine, we use different devices to move charges in the body with the overall goal of increasing energy and life-force.

Energy comes in different forms as shown in this chart. Most energy medicine devices are electromagnetic in Nature so we will focus on 3 main types of electromagnetic energy in this module. 1) Electrical Energy 2) Magnetic Energy 3) Light Energy. Though all are connected within the ONE electromagnetic force, they ARE all different in their properties and healing power (as we'll see in this course).

**Particles and Waves**

Classical or Newtonian Physics divides the physical world in particles and waves. Only quantum mechanics resolves the two as ONE.

Particles transport energy (and momentum)

**with their mass**and motion from one point to another in space.

Waves transport energy from one place to another without mass (via frequency resonance and amplitude).

Basically Particles like electrons have mass and waves (aka photons) do not. So in energy medicine, food, water, air for example would be particle-like forms of energy medicine as they all have mass (weight of air in refrigerator is a grapefruit). Energy is transferred mainly by the particles of food, liquid or air. While light, magnetism and electric fields are more wave-like in that energy is transfer happens with virtual or light photons (massless).

Most energy medicine devices use time varying electric or magnetic fields or electromagnetic waves like Radio, Infrared, Light and UV which are more wavelike and field based, So lets begin with a basic understanding of Waves.

**Classical Wave Theory - Great starting point for Understanding Energy Medicine.**

All life is oscillating or in vibration. Light is a vibration, Seeing, hearing, touching, smelling and tasting is all vibration. Oscillations or vibrations are more technically called waves in science. These waves have four fundamental characteristics.

A wave is a disturbance of some sort that propagates through space and transports some kind of energy from one point to another

A wave is a generic term for a pattern that repeats itself over time -- sound waves, brain waves, water waves in a pond, ocean waves, light waves, magnetic waves, etc are all repeating patterns. One cycle of a wave is the portion of the wave that repeats.

We will mainly look at Electromagnetic Waves which require no medium to propagate (unlike sound and water waves). But in understanding the basic properties of waves it is helpful to draw analogies with sound and water waves as they are easier to visualize. All electromagnetic waves travel the same speed in a vacuum, the speed of light.

A wave is a disturbance of some sort that propagates through space and transports some kind of energy from one point to another

**without**transporting mass.A wave is a generic term for a pattern that repeats itself over time -- sound waves, brain waves, water waves in a pond, ocean waves, light waves, magnetic waves, etc are all repeating patterns. One cycle of a wave is the portion of the wave that repeats.

We will mainly look at Electromagnetic Waves which require no medium to propagate (unlike sound and water waves). But in understanding the basic properties of waves it is helpful to draw analogies with sound and water waves as they are easier to visualize. All electromagnetic waves travel the same speed in a vacuum, the speed of light.

**Defining Wave Characteristics**

**1)**(or Intensity) The maximum amount of disturbance during a wave cycle.

__Amplitude__:Amplitude is the height of the wave. Classically the Amplitude relates to the Energy in the wave**. A greater amplitude has more energy like loudness or brightness.

Our ears perceive high amplitude as loud. The louder the sound is - the more energy it has. Our ears perceive low amplitude as soft or quiet. The quieter the sound is - the less energy it has.

Our eyes perceive high amplitude as bright light. The brighter it is, the more energy it has. Our eyes perceive low amplitude as dim light. The dimmer light is, the less energy it has.

**actually it is |A^2| the amplitude squared that is the energy.

**2)**Denoted by the symbol λ (Lambda), this is the distance between two consecutive crests (peaks) or two consecutive troughs (valleys) of a periodic wave (wave that repeats itself). The distance equal to the wavelength makes one cycle of change.

__Wavelength__:Wavelength is the length of the wave.

**3)**The Frequency

__Frequency:__*f,*is the number of cycles per unit time a wave repeats at a given point. The frequency is measured in Hertz (Hz) named after the physicist Heinrich Hertz and equals the number of times the signal repeats itself in one second (the cycles per second).

Our ears perceive high frequency as high pitch, or as a high note. The higher the note, the more energy it has. Our ears perceive low frequency as a low pitch, or as a low note. The lower the note, the less energy it has.

Our eyes perceive high frequency as violet (though the frequency could go much higher - but would be invisible to our eyes). Our eyes perceive low frequency as red (though the frequency could go much lower - but would also be invisible to our eyes).

In Quantum Physics E=hv , so the higher the frequency, the more energy the wave has.

We'll come back to Electromagnetic Waves AT The end of this video and in other modules look at more complex types of waves but this serves as a simple introduction to the idea of a wave which is the primary way most energy medicine devices transfer energy from one point to another.

To Understand Electromagnetic Waves and PEMF Therapy, it is important to understand Electricity and Magnetism, which means we first need to understand what charge is. Charges like electrons and protons are THE SOURCE for ALL electromagnetic phenomenon. We'll break this up into four parts:

I. Electrostatics - Charges at Rest

II. Charges in Motion Part 1 (Circuits)

III. Charges in Motion Part 2 - Magnetism and Magnetostatics

IV. Charges in Motion Part 3 - Time Varying Magnetic Fields (PEMFs) & Magnetic Induction

V. - Maxwells Equations & Electromagnetic Waves (Putting it all together and come FULL CIRCLE).

I. Electrostatics - Charges at Rest

II. Charges in Motion Part 1 (Circuits)

III. Charges in Motion Part 2 - Magnetism and Magnetostatics

IV. Charges in Motion Part 3 - Time Varying Magnetic Fields (PEMFs) & Magnetic Induction

V. - Maxwells Equations & Electromagnetic Waves (Putting it all together and come FULL CIRCLE).

Perhaps you have walked across a carpet on a dry day and reached out your hand to touch doorknob 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, persons were familiar with four 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

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.

Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a negative charge, if there are fewer it will have a positive charge, and if there are equal numbers it will be neutral.

First thing is: q is conserved. Conserved is a physics terms for saying — does not change with time

Charge is quantized; 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.

So charge is granular, not continuous.

All things carrying electric charge in our world in daily life are either protons or electrons. The charge of the neutron, as you can guess, is 0. The charge of the electron, by some strange convention, was given this minus sign by Franklin. And the charge of the proton is plus 1.6^-19 coulombs.

Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a negative charge, if there are fewer it will have a positive charge, and if there are equal numbers it will be neutral.

First thing is: q is conserved. Conserved is a physics terms for saying — does not change with time

Charge is quantized; 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.

So charge is granular, not continuous.

All things carrying electric charge in our world in daily life are either protons or electrons. The charge of the neutron, as you can guess, is 0. The charge of the electron, by some strange convention, was given this minus sign by Franklin. And the charge of the proton is plus 1.6^-19 coulombs.

**I. Electrostatics - Charges at Rest**

Force of Electrostatics...

Force of Electrostatics...

**Electrostatic Force**

I’m able to lift paper with comb. Now, that’s not the force of gravity because gravity doesn’t care if you comb your hair or not, okay? And also when I shake it, it falls down.

10^40 stronger gravity.

Everything is acting against me, and I’m able to triumph against all of that with this tiny comb.

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 quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them.

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 proton anywhere in the universe is identical.

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 proton anywhere in the universe is identical.

**Electric Field**

Define F = qE

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.

Michael Faraday came up with the idea of a field (working with magnets). 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 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).

An electric field (sometimes abbreviated as E-field) is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. 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.

Now, what’s the importance of the electric field? Whereas q1 and q2 exist only at these two places,

Field is like sound of one hand clapping. Don't need 2 charges, just one. Something is really different at location when q is present.

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.

Michael Faraday came up with the idea of a field (working with magnets). 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 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).

An electric field (sometimes abbreviated as E-field) is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. 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.

Now, what’s the importance of the electric field? Whereas q1 and q2 exist only at these two places,

**the electric field can be defined everywhere**.Field is like sound of one hand clapping. Don't need 2 charges, just one. Something is really different at location when q is present.

**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.

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.

**Gauss's Law**

The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity.

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. That is, it defines the Electric Field just like E = F/q, BUT it is much simpler for calculations (that is, it is a mathematical tool).

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

The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field. Gauss's Law is a general law applying to any closed surface. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.

Another way of visualizing this is to consider a probe of area A which can measure the electric field perpendicular to that area. If it picks any closed surface and steps over that surface, measuring the perpendicular field times its area, it will obtain a measure of the net electric charge within the surface, no matter how that internal charge is configured.

Another way of visualizing this is to consider a probe of area A which can measure the electric field perpendicular to that area. If it picks any closed surface and steps over that surface, measuring the perpendicular field times its area, it will obtain a measure of the net electric charge within the surface, no matter how that internal charge is configured.

**Gauss Simple Overview:**Take the field of a point charge q and compute its surface integral on a sphere centered on it. The answer is q/eo independent of the radius of the sphere because the area of the sphere went as r^2 while the field decreased by 1/r^2. Furthermore the surface integral is the same on any closed surface enclosing the charge. Finally use superposition to show that the surface integral of E on any closed surface was the total charge enclosed divided by eo.**Voltage (or Electrical Potential)**

The electrical potential (Voltage) difference between 2 points A and B is the work required to move one unit of Charge (Coulomb), from point A to point B in space. This is called Electrical Potential or Voltage because it is measure in volts. Once the charges are separated like in a battery, there is stored energy available to do work.

Since force is measured in newtons and charge in coulombs, electric field is in units of Newtons per coulomb. Voltage is measured in newton meters per coulomb since Work = force * distance.

V(B) - V(A) = W/Q (Voltage difference between two points = Work done per unit charge.

W=QV(r)

**W=QV(r)**

Potential IS potential energy (the work it takes to create a system) per unit charge (just as the field is the force per unit charge.

Voltage is like the "pressure" electronics have to go somewhere. They might not be going anywhere at any particular time, but the pressure is still there.

Potential IS potential energy (the work it takes to create a system) per unit charge (just as the field is the force per unit charge.

Or you can think of Voltage is kinda like elevation, it is the difference between two levels and the reference point needs to be set (like sea level).

**Capacitance**

Capacitance is the amount of energy stored in a system, called a capacitor, per unit of electric potential or voltage. A capacitor is measured in Farads (Coulomb per volt).

C = Q/V

So a capacitor can be looked upon as a device that stores energy (or Voltage).

Note: to charge a capacitor (or a battery for that matter), you have to remove electrons from the positive plate and carry them to the negative plate. In doing so you fight against the electric field (which of course requires work to do this).

So it always takes energy of some force to separate charge, but once separated, across an insulator (like air), there is energy stored that can do work when needed.

Batteries store energy in a similar way by separating charge, as does the cell membrane in each cell (acts like a spherical capacitor pumping charges with Sodium potassium pump, mitochondria. ATP also separates charge across the double bond.

Also water in it's 4th phase separates charge (via light) and can store energy.

Separating Charge is ONE OF THE KEYS to energizing not only electronics, but life itself!

C = Q/V

So a capacitor can be looked upon as a device that stores energy (or Voltage).

Note: to charge a capacitor (or a battery for that matter), you have to remove electrons from the positive plate and carry them to the negative plate. In doing so you fight against the electric field (which of course requires work to do this).

So it always takes energy of some force to separate charge, but once separated, across an insulator (like air), there is energy stored that can do work when needed.

Batteries store energy in a similar way by separating charge, as does the cell membrane in each cell (acts like a spherical capacitor pumping charges with Sodium potassium pump, mitochondria. ATP also separates charge across the double bond.

Also water in it's 4th phase separates charge (via light) and can store energy.

Separating Charge is ONE OF THE KEYS to energizing not only electronics, but life itself!

Materials such as metals like copper and silver, that permit the free flow of electrons are called conductors.

Materials such as glass, fabric, plastic and rubber that do not allow free flow of charge are called insulators.

**Conductors**

Contain an unlimited supply of charges that are free to move about through the material. This means that many of the electrons (one or two per atom in a typical metal) are not associated with any particular nucleus, but roam around at will.

NOTE: Electric Fields in Conductors are Zero because the free charges all balance out to create an opposing electric field.

Negative Charges migrate to cancel the field (negative charges

Charges remain on surface UNLESS a strong field, then you can have corona discharge (lightning).

By Contrast, Insulators (also called Dielectrics), all charges are attached to specific atoms or molecules - they're on a tight lease, and all they can do is move a bit with the atom of molecule.

**The atoms an molecules will be polarized or little dipoles will be set up like image below. Neutral atoms have no dipoles built in but Molecules can (polar molecules LIKE WATER). Polar molecules have charge separation where the positive and negative charges are pulled away from each other (depends on dipole moment).

**The atoms an molecules will be polarized or little dipoles will be set up like image below. Neutral atoms have no dipoles built in but Molecules can (polar molecules LIKE WATER). Polar molecules have charge separation where the positive and negative charges are pulled away from each other (depends on dipole moment).

When a substance is filled with a homogeneous dielectric (or insulator), the field everywhere is reduced by a factor of 1 over the dielectric constant.

It is not that anything is wrong with Coulombs law, rather the polarization of the medium partially "shields" the charge, by surrounding it with a charge of the opposite sign.

The greater the dielectric constant the MORE the electric field is SHIELDED by a charge of the opposite sign.

In fact Coulombs law stays the same, you just divide by the dielectric constant.

NOTE: Coulombs law is for a vacuum and air is very close to 1, so the answers still work out in a laboratory between charged objects separated by air (see below). Water on the other hand would shield the electric force by 80 fold (divide by 80). So the human body which is mostly water is NOT at all transparent to Electric fields (unlike magnetic fields which go right through).

It is not that anything is wrong with Coulombs law, rather the polarization of the medium partially "shields" the charge, by surrounding it with a charge of the opposite sign.

The greater the dielectric constant the MORE the electric field is SHIELDED by a charge of the opposite sign.

In fact Coulombs law stays the same, you just divide by the dielectric constant.

NOTE: Coulombs law is for a vacuum and air is very close to 1, so the answers still work out in a laboratory between charged objects separated by air (see below). Water on the other hand would shield the electric force by 80 fold (divide by 80). So the human body which is mostly water is NOT at all transparent to Electric fields (unlike magnetic fields which go right through).

**II. Charges in Motion Part 1 (Circuits)**

Circuits and Electric Currents

1) Current (I)

2) Resistance (R)

3) Voltage (V)

4) Power (P)

**Current (I):**

The first thing in electrical circuits is, you’ve got some wire and you’ve got an electric current flowing in it. We need a description of the current.

The current is defined as follows. Imagine this is the perfect cylinder, cross section A. You cut it somewhere and you watch all the charges go by, and you see the number of coulombs that go by per second. That’s called the electric current and is measured in amperes. So 1 coulomb per second is 1 amp.

Or simply put, Electric Current is the rate of flow of an electric charge per unit time and is measure in Amperes (Coulombs/second).

and can be defined by the equation

I = Q/t

in this equation, I is the current and Q is the amount of charge (dQ) that flowed past a point in time t (dt).

and can be defined by the equation

I = Q/t

in this equation, I is the current and Q is the amount of charge (dQ) that flowed past a point in time t (dt).

2) Resistance (R)

Resistance is a measure of opposition offered by a material to the flow of charge through it. Resistance can be measure in a circuit by

I = V/R

What this means is that the larger the resistance, the smaller the current. Resistance is measured in units of the Ohm.

Resistance (R): Resistance, sometimes referred to as Impedance, is the measurement of how much a conductor resists electrons. Conductors are not perfect, and most will have some natural loss. This loss is called Resistance. Resistance slows down the flow of electrons in the circuit, limiting an otherwise stronger flow, to a more manageable trickle.

Resistance is a measure of opposition offered by a material to the flow of charge through it. Resistance can be measure in a circuit by

I = V/R

What this means is that the larger the resistance, the smaller the current. Resistance is measured in units of the Ohm.

Resistance (R): Resistance, sometimes referred to as Impedance, is the measurement of how much a conductor resists electrons. Conductors are not perfect, and most will have some natural loss. This loss is called Resistance. Resistance slows down the flow of electrons in the circuit, limiting an otherwise stronger flow, to a more manageable trickle.

Part of the resistance in a circuit is from the geometry of the wire itself, mainly the length and cross sectional area of the wire.

*This will have an important consequence in PEMF therapy devices as the "good" ones use copper wire. BUT cheaper PEMF companies use THIN wire which has a greater resistance, more heat loss and yields signal that is not clear.

*This will have an important consequence in PEMF therapy devices as the "good" ones use copper wire. BUT cheaper PEMF companies use THIN wire which has a greater resistance, more heat loss and yields signal that is not clear.

**3) Voltage Revisited (in relation to circuits).**

Once Charges are Separated, the Voltage Represents Stored ENERGY!! (think Battery)

Once Charges are Separated, the Voltage Represents Stored ENERGY!! (think Battery)

Voltage is the term used to describe electrical pressure or electromotive force (EMF).

A battery can create and store voltage or electrical pressure. Voltage is a relative measure of how strongly a charge will be pushed away from or towards a location of the potential.

A battery has a build up of negative charge at one terminal and positive charge at the other. These charges want to balance out, so there is an electrical force, or strain, between them.

When a circuit is connected between the terminals of a battery, the electrical pressure (voltage) from the battery forces electrons to flow from the negative terminal to the positive terminal.

In a battery, electrons are chemically separated out to the (-) side and prevented from leaking on to the (+) side through the inside.

So there's pressure built up for electrons to move from - to + around a circuit.

Between the positive and negative terminals of the battery there are some chemicals that essentially remove electrons from the positive terminal and deposit them on the negative terminal. Finally chemical forces balance electrostatic field and final voltage is reached.

**4) Power**: Power is the measurement of the rate at which work is actually being preformed by the electrical circuit. This is measured in Watts (joules/sec). The units are energy per unit time. This can also be compared with Horsepower (1W = 0.0013 HP) and BTU’s (1W = 3.414 BTU/h).

**Ohm’s Law:**

The above four properties are all fundamental in diagnosing and designing electrical circuits. With only two of the above values, you can figure out any other value. This is ohm’s law.

V = I*R

I = V/R

R = V/I

P = V*I or P = (I*I)*R

A voltage of One Volt, will force a current of One Amp, through a resistance of One Ohm, which will create One Watt of power!

The water analogy sums it up nicely. The water level, or back pressure, is comparable to Voltage. The tap is comparable to Resistance. The stream of water is comparable to Current, and the Turbine is comparable to Power.

**Analogy to the body...**

Microcirculation - heart is the source of energy...

Current is energy flow whether the current is charge (nervous system) or water (blood/lymph).

R = viscosity*length/cross sectional area

Thick blood and small vessels (blocked by bad circulation) increases resistance.

Increased resistance puts back pressure on heart and leads to poor nutrient delivery and detox.

**III. Charges in Motion Part 2 - Magnetism and Magnetostatics**

Simple Experiments with Horseshoe magnets, bar magnets, neodynium magnets.

Stationary Charges produce electric fields that are constant in time; hence the term electrostatics. As we'll see steady currents produce magnetic fields that are constant in time; this is called

Stationary Charges produce electric fields that are constant in time; hence the term electrostatics. As we'll see steady currents produce magnetic fields that are constant in time; this is called

**magnetostatics.**Magnetism was first discovered in the ancient world, when people noticed that lodestones, naturally magnetized pieces of the mineral magnetite, could attract iron.

1263 Pierre de Maricourt mapped out the magnetic field of a lodestone with a compass. He discovered that a magnet has two magnetic poles a North and a South.

The Englishman William Gilbert (1540-1603) was the first to investigate the phenomenon of magnetism systematically using scientific methods. He also discovered that

An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Ørsted who discovered by the accidental twitching of a compass needle near a wire that an electric current could create a magnetic field.

Carl Friedrich Gauss; Jean-Baptiste Biot and Félix Savart, both of whom in 1820 came up with the Biot–Savart law giving an equation for the magnetic field from a current-carrying wire; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism

1263 Pierre de Maricourt mapped out the magnetic field of a lodestone with a compass. He discovered that a magnet has two magnetic poles a North and a South.

The Englishman William Gilbert (1540-1603) was the first to investigate the phenomenon of magnetism systematically using scientific methods. He also discovered that

**Earth**is itself a weak magnet.An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Ørsted who discovered by the accidental twitching of a compass needle near a wire that an electric current could create a magnetic field.

Carl Friedrich Gauss; Jean-Baptiste Biot and Félix Savart, both of whom in 1820 came up with the Biot–Savart law giving an equation for the magnetic field from a current-carrying wire; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism

**Magnetism**is a property of a material that enables two objects to exert a special kind of force (called the Lorenz force) on each other called the magnetic force,

**which is created by an electric charge in motion.**

The phenomenon of magnetism is "mediated" by the magnetic field.

A

**magnetic field**is a field produced by a moving charge that is used to exert a magnetic force on another moving charge. (Which is easy to visualize with iron filings).

**Magnetic Force Law**

Whereas stationary charges produce an electric field, moving charges in addition produce a magnetic field. In fact magnetic fields are easier to detect, all you need is a boy scout compass. Now if you hold a tiny compass in the vicinity of a current carrying wire, you quickly discover a peculiar thing:

The field does not point toward the wire nor away from it, but rather it circles around the wire. In fact if you grab the wire with your right hand - thumb in the direction of current - your fingers curl around in the direction of the magnetic field (

**Right Hand Rule**).

When a charged particle moves through a magnetic field B, it feels a

**Lorentz force**F given by the cross product:

F = q (v x B)

q is the electric charge of the particle, and

v is the velocity vector of the particle

In the Presence of both electric and magnetic fields the total force is F = Q[E + v x B).

It is a velocity dependent nonconservative force because the force is perpendicular to the direction of motion. Work equation Work = Force * Distance is ONLY done in direction of moving. So it can ALTER the path of a particle, but does not do work.

When you place a source charge next to a moving current, nothing happens. Why you might ask as there is a current and obviously electrons moving in the wire.

**Well, in a metal there are just as many stationary plus charges as moving minus sign charges.**

But if you move the source charge, then something HAPPENS!

Consider the experiment of two parallel wires with current moving in opposite directions. We find the wires repel. But if the current is moving in the same direction, the wires attract. Because both wires are electrically neutral (which is obvious when the current is turned off), it is not electrostatics (so Coulombs law does not apply).

This is THE MAGNETIC FORCE!

So magnetism is caused by moving charges and FELT by moving charges!

Magnetostatics is two parts

1) the force felt by a moving charge

2) Specifying how currents produce a magnetic field

**Magnetic Forces In Action**

An electromagnet is a type of magnet in which the magnetic field is produced by an electric current through a tight wound current loop with many turns.

The magnetic field disappears when the current is turned off.

NOTE: It is Important to closely space the turns or the field lines bleed out and you loose the PURENESS of the magnetic field through the center of the loops, not to mention the strength -

MANY PEMF DEVICES DO NOT USE TIGHTLY WOUND COILS WHICH IS BAD PHYSICS.

Some Pemf applicators like iMRS probe, the wire turns are often wound around a magnetic core made from a ferromagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet. Electromagnets usually utilize this as well.

Electromagnets are widely used as components of other electrical devices, such as motors, generators, relays, solenoids, loudspeakers, hard disks, MRI machines, scientific instruments, and magnetic separation equipment. Electromagnets are also employed in industry for picking up and moving heavy iron objects such as scrap iron and steel.

THEY ALL USE LOOPS OF CURRENT - PERFECTLY CIRCULAR!!

So we have been talking about magnetic forces acting on moving charges, let's now look at how the magnetic field is generated by (you guessed it), moving charges.

NOTE: In physics these are the two primary things we look at, the fields produced (by charges, masses, etc) and the forces acting on test masses or charges. This is how field theories are framed.

**Ampere's Law and Biot Savart Law**

Just like the electric field, a magnetic field is also represented by field lines, which give rise to the concept of magnetic flux. The flux is a measure of the magnetic field lines through a certain area which is proportional to the strength of the magnetic field and the surface under consideration.

But unlike electric charges, there is no such thing as isolated magnetic charges (magnetic monopoles).

In other words, unlike electric field lines that begin and end on electric charges, magnetic field lines never have end points,

**they always form closed loops.**

Both the Electric Force and Magnetic Force are Inverse Square Laws, but the inverse square only applies to point charges or spheres or blobs of localized charge. Never happens with magnetic fields because as we'll see there are no SOURCE magnetic monopoles and even spherical magnets have a north and south pole. SO YOU'LL NEVER SEE A 1/R^2 Dropoff in magnetic fields, NEVER! This is important to note as many so called PEMF experts USE THIS BAD SCIENCE TO JUSTIFY HIGH INTENSITY (more on this later).

Typically electric forces are enormously greater than magnetic ones. Has to due with the fundamental constants eo and uo.

The reason the magnetic force can dominate in a current of wire is that the overall charge of the wire is electrically NEUTRAL... that is, in metals electrons can move free around BUT the protons and positive charges exactly balance it out.

So in true PEMF devices that use a current carrying circular loops, the MAGNETIC component is the STRONGEST just like static magnetics!! A current loop is almost PURE MAGNETIC FIELD LINES IN THE CENTER OF THE LOOP!!!

There is a difference though as PEMF currents change with time (and are not magnetostatics) which we will see when we look at electromagnetic induction. But the Biot Savart Law is STILL a very good approximation for measuring the intensity of the field a point a distance above the mat.

Biot Savart Law is one Nasty Formula in its Vector Form (vs Coulombs Law).

Whereas the cause of the electric field is a POINT charge, the cause of the magnetic field is charge in motion which introduces a velocity vector.

ISOMORPHISM of COULOMBS AND BIOT SAVART

The actual forces in both electrostatics and magnetostatics depend on the charge and current arrangements and distributions. 1/r^2 is only for point charges and spheres/blobs.

A few examples of how Forces depend on the geometry of the charge/currents. Note geometrical ISOMORPHISM of both electric and magnetic fields!

1) Point or sphere of charge is a 1/r2 dropoff (no equivalent in magnetostatics or PEMF).

2) Infinite (or long) Line of Charge AND a line of current are both 1/r dropoffs

3) Infinite plane of charge or current never drop off (always the same)

Important Note Using the Biot Savart to Calculate PEMFs

Because the Law is for steady currents that do not change according to an ammeter) , the calculations are only approximately correct for PEMFs, but still VERY close (I have verified the Biot Savart Law with a Magnetic Field Detector on the IMRS and it is just about perfect for peak magnetic fields.

This is called a quasistatic approximation but it is very close in measuring the B fields through PEMF current loops.

Whereas the cause of the electric field is a POINT charge, the cause of the magnetic field is charge in motion which introduces a velocity vector.

ISOMORPHISM of COULOMBS AND BIOT SAVART

The actual forces in both electrostatics and magnetostatics depend on the charge and current arrangements and distributions. 1/r^2 is only for point charges and spheres/blobs.

A few examples of how Forces depend on the geometry of the charge/currents. Note geometrical ISOMORPHISM of both electric and magnetic fields!

1) Point or sphere of charge is a 1/r2 dropoff (no equivalent in magnetostatics or PEMF).

2) Infinite (or long) Line of Charge AND a line of current are both 1/r dropoffs

3) Infinite plane of charge or current never drop off (always the same)

**4) RING of Charge and a RING of current are in Inverse 3/2 dropoff (NOT A 1/r2!!). We'll explore this later as TRUE PEMF devices use a ring of charge.**

The current loop is so fundamental to magnetism that even at the atomic magnetic fields are produces by little current loops. (flat coil)

5) Infinite Solenoid also important. The magnetic field is uo*n*I inside the solenoid and ZERO outside... (tower of coil).

NOTE: Pure Magnetic field is MAINLY in the center of the current loops ... NOT MUCH OUTSIDE. A true PEMF device should have large PURE copper coil loops to apply to whole body along with local applicators. In each case center of loop should be placed on the Spot!The current loop is so fundamental to magnetism that even at the atomic magnetic fields are produces by little current loops. (flat coil)

5) Infinite Solenoid also important. The magnetic field is uo*n*I inside the solenoid and ZERO outside... (tower of coil).

NOTE: Pure Magnetic field is MAINLY in the center of the current loops ... NOT MUCH OUTSIDE. A true PEMF device should have large PURE copper coil loops to apply to whole body along with local applicators. In each case center of loop should be placed on the Spot!

Important Note Using the Biot Savart to Calculate PEMFs

Because the Law is for steady currents that do not change according to an ammeter) , the calculations are only approximately correct for PEMFs, but still VERY close (I have verified the Biot Savart Law with a Magnetic Field Detector on the IMRS and it is just about perfect for peak magnetic fields.

This is called a quasistatic approximation but it is very close in measuring the B fields through PEMF current loops.

**Current Loops**

What is common among a doorbell, an electric motor, and electromagnet (like at junkyards), a transformer AND PEMF devices (the REAL ONES)?

ANS: All contain coils of wires with a large number of turns spaced closely enough that each turn closely approximates a planar circular loop of current.

Each loop of current , I, generates a magnetic field according to a rule called the right hand rule (and more Precisely by Ampere's Law).

**Magnetic Dipoles**

A very common source of magnetic field found in nature is a dipole, with a "South pole" and a "North pole", terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field.

Since a bar magnet gets its ferromagnetism from electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. A bar magnetic is called a dipole because it has two poles (the prefix di- means two). If you cut bar magnet in half, it creates two more magnets.

There are no magnetic monopoles (at least not discovered yet). Magnetic sources (magnets , current loops, etc) always come in pairs of N and S.

In electostatics, both a positive charge AND a negative charge can be monopoles. An electric dipole is formed from two separated electric charges (of opposite charge).

Note the similarity of the fields of electric and magnetic dipoles (when idealized they are the same geometry), that of a toroidal field or donut shape (in 3D). You may have heard how the Torus is a fundamental geometry in the universe.

Note the similarity of the fields of electric and magnetic dipoles (when idealized they are the same geometry), that of a toroidal field or donut shape (in 3D). You may have heard how the Torus is a fundamental geometry in the universe.

**You Cannot Shield Magnetic Fields (like you can with electric fields).**

Magnetic fields (forces are caused by magnetic fields) cannot be blocked, no. That is, there is no such thing as a magnetic insulator.

This is because there are no magnetic monopoles. That is, where as you can separate electric monopoles (positive and negative charges) such that an E-field never has to terminate on the opposite charge, you cannot do this with magnetic poles.

There is no such thing as "magnetic charge." All magnetic field lines MUST TERMINATE on the opposite pole. Because of this, there is no way to stop them - nature must find a way to return the magnetic field lines back to an opposite pole.

Even LEAD does not block magnetic fields.

**However**, magnetic fields can be re-routed around objects. This is a form of magnetic shielding. By surrounding an object with a material which can "conduct" magnetic flux better than the materials around it, the magnetic field will tend to flow along this material and avoid the objects inside. This allows the field lines to terminate on the opposite poles, but just gives them a different route to follow.

Now suppose I stack a whole lot of loops coaxially, say by wrapping a wire around a cardboard cylinder many times into a spiral (like a solenoid). Given that a single loop produces a dipole field, we get a field that looks like the solenoid (which is an electromagnet depicted here. This field ALSO looks exactly like a bar magnet as we pointed out earlier. As far as a compass needle is concerned, the fields are identical.

So how does the permanent magnet work? Is it a different kind of magnetism?

NO, everything is coming from electric currents. In the case of the permanent magnet, the currents are coming from the electrons in the atoms. Every atom has electrons going around the nucleus, and every moving electron is a current.

Imagine for simplicty nine electrons going around their atoms in the plane of a piece of paper shown here. The region in between the atoms they go in opposite directions. They CANCEL. The ONLY thing that does not cancel is the current along the perimeter or edge. THUS, a single layer of atoms can produce a current at the edge. It will be permanent since atomic currents are.

Now think of a magnetic solid consisting of many layers of such atoms. At the edge of each layer is its current. So a magnetic material can effectively have a sheet of current on its surface, which will produce a magnetic field. In the case of the cylindrical magnet shown here, the currents move EXACTLY like the solenoid or electromagnet with currents circulating around it and by the Right hand rule, the magnetic field is exactly what you would expect from a bar magnet. So even STATIC magnets are produced from CIRCULATING currents!!

NO, everything is coming from electric currents. In the case of the permanent magnet, the currents are coming from the electrons in the atoms. Every atom has electrons going around the nucleus, and every moving electron is a current.

Imagine for simplicty nine electrons going around their atoms in the plane of a piece of paper shown here. The region in between the atoms they go in opposite directions. They CANCEL. The ONLY thing that does not cancel is the current along the perimeter or edge. THUS, a single layer of atoms can produce a current at the edge. It will be permanent since atomic currents are.

Now think of a magnetic solid consisting of many layers of such atoms. At the edge of each layer is its current. So a magnetic material can effectively have a sheet of current on its surface, which will produce a magnetic field. In the case of the cylindrical magnet shown here, the currents move EXACTLY like the solenoid or electromagnet with currents circulating around it and by the Right hand rule, the magnetic field is exactly what you would expect from a bar magnet. So even STATIC magnets are produced from CIRCULATING currents!!

**Magnetism, at its root, arises from CURRENT LOOPS!**

1) Electric currents in wires and current loops (dipoles). Earth's current is in essence a gigantic current loop (dynamo theory of earth's magnetic field).

2) Spin magnetic moments of elementary particles --> Gives rise to magnetic materials.

The magnetic properties of materials are mainly due to the magnetic moments of their atoms' orbiting electrons (little electrons orbiting nucleus (current LOOPS) all aligned in bar magnets!).

So ALMOST ALL MAGNETIC PHENOMENON ARE DUE TO PERFECTLY CIRCULAR CURRENT LOOPS!! This is VITALLY IMPORTANT TO UNDERSTAND IN RELATION TO PEMF DEVICES BECAUSE AS WE'LL SEE THE QUALITY OF THE MAGNETIC FIELD PRODUCES DEPENDS ON THE QUALITY OF THE CURRENT LOOPS. If there are NO CURRENT LOOPS THERE IS NO PURE MAGNETIC FIELD OR PEMF FIELD!!

**Curie Temperature**

So you may ask, why is not everything magnetic?

Most atoms have electron pairs that CANCEL as we'll see next. Only certain atoms and materials have enough single outer shell electrons that are unpaired so the spins do not cancel.

Even if an atom has some uncancelled magnetic moment, the moments from different atoms may point in random directions, adding up to nothing. The random orientation is a reflection of thermal agitation. Things like to jiggle when you heat them. If you take a bar magnet on your fridge and put it on a hotplate for a while, you will find it becomes less magnetic. And if you heat it above the Curie Temperature, the jiggling will be so intense the magnetism is destroyed. But if you cool it below the Curie temperature, the magnetism will be restored.

BUT restoring the magnetic field only works in the presence of an external field.

Only in ferromagnetic materials below the Curie temperature, the dipoles remain aligned even after the external field is removed. Why? The dipoles all lined up produce their own magnetic field that is strong enough to keep them aligned EVEN after the external field is removed. It pulls itself up by its own bootstraps. Thus magnetism is a cooperative effect. If can exist ONLY if the thermal agitation is not too strong to kill the ordering tendency of generated by the diploes themselves.

If You ask the average person what is magnetism, you will probably be told about your refrigerator decorations, compass needles or the North Pole - none of which has any obvious connection with moving charges or current carrying wires.

Yet, ALL magnetic phenomenon are due to electric charges in motion, and in fact if you could examine a piece of magnetic material on the atomic scale you would find tiny currents, electrons spinning on axis and orbiting nucleus.

These little current loops are so small we can treat them as pure magnetic dipoles.

When a significant portion of the atomic dipoles line up in the same direction, the material becomes MAGNETIZED.

Think of nuclei and electrons as tiny spinning magnets. When nuclear and electron spins in a material orient in the same direction as the magnetic field, their individual magnetic moments locally augment the field. This augmentation of the external field is called paramagnetism. Subatomic particles may also create magnetic effects that oppose the applied field; this is called diamagnetism.

Few Materials like Iron, retain their magnetism even after the external field is removed. These are called Ferromagnets -iron, nickel cobalt and certain alloys - (or permanent magnets - though it is never permanent due to thermal and vibrational effects). These magnets will always have a STATIC magnetic field. Only PEMF type of devices can create therapeutic changing magnetic fields (as we'll see).

Yet, ALL magnetic phenomenon are due to electric charges in motion, and in fact if you could examine a piece of magnetic material on the atomic scale you would find tiny currents, electrons spinning on axis and orbiting nucleus.

These little current loops are so small we can treat them as pure magnetic dipoles.

When a significant portion of the atomic dipoles line up in the same direction, the material becomes MAGNETIZED.

Think of nuclei and electrons as tiny spinning magnets. When nuclear and electron spins in a material orient in the same direction as the magnetic field, their individual magnetic moments locally augment the field. This augmentation of the external field is called paramagnetism. Subatomic particles may also create magnetic effects that oppose the applied field; this is called diamagnetism.

Few Materials like Iron, retain their magnetism even after the external field is removed. These are called Ferromagnets -iron, nickel cobalt and certain alloys - (or permanent magnets - though it is never permanent due to thermal and vibrational effects). These magnets will always have a STATIC magnetic field. Only PEMF type of devices can create therapeutic changing magnetic fields (as we'll see).

Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field.

Ferro > (suprapara)> Para > DIA (see above).

Ferro > (suprapara)> Para > DIA (see above).

Most biological tissues are weakly diamagnetic, meaning most of our tissues cannot be magnetized even while a magnetic field is applied (but the magnetic fields DOES influence moving charges and ions in the body, but that is different.)

However, some tissues contain focal accumulations of metals such as iron, gadolinium, copper, or manganese that concentrate the magnetic field and are therefore paramagnetic. A few tissues also contain chunky iron-based protein conglomerates (ferritin and hemosiderin) that are superparmagnetic.

BUT there are trace amounts of magnetite (which is ferromagnetic) that may not contribute to bulk susceptibility, BUT studies have shown the body can amplify weak magnetic and electric fields, so perhaps it does play an important role in coupling our body to the earth's magnetic field.

Also noteworthy for PEMF applicator, many extrinsic metallic foreign bodies and surgical implants are ferromagnetic, and these are commonly encountered in MRI imaging. Titanium is much less susceptible. But no (non-electronic) implants are contraindicated for low frequency, low intensity PEMF therapy.

However, some tissues contain focal accumulations of metals such as iron, gadolinium, copper, or manganese that concentrate the magnetic field and are therefore paramagnetic. A few tissues also contain chunky iron-based protein conglomerates (ferritin and hemosiderin) that are superparmagnetic.

BUT there are trace amounts of magnetite (which is ferromagnetic) that may not contribute to bulk susceptibility, BUT studies have shown the body can amplify weak magnetic and electric fields, so perhaps it does play an important role in coupling our body to the earth's magnetic field.

Also noteworthy for PEMF applicator, many extrinsic metallic foreign bodies and surgical implants are ferromagnetic, and these are commonly encountered in MRI imaging. Titanium is much less susceptible. But no (non-electronic) implants are contraindicated for low frequency, low intensity PEMF therapy.

**Ampere's Law**

Ampere's law is to Magnetostatics what Gauss's law was to electrostatics.

**Review Gauss**: we took the field of a point charge q and computed its surface integral on a sphere centered on it. We found the answer was q/eo independent of the radius of the sphere because the area of the sphere went as r^2 while the field decreased by 1/r^2. Furthermore the surface integral was the same on any closed surface enclosing the charge. Finally we used superposition to show that the surface integral of E on any closed surface was the total charge enclosed divided by eo.

Now for Ampere. Consider the field B due to an infinite wire carrying current I. The current to the right like pictured through right hand rule magnetic field will circulate around the as shown. Consider a line integral around this loop, called the circulation. The line integral or circulation is independent of the radius of the circle. This is analogous to Gauss, only it is a circle not a sphere. Or more general, it works for any contour just as Gauss works for any surface.

The line integral of B around any closed path equals uo times the current enclosed. This works with superposition of many currents just as Gauss's law works for a collection of many charges.

To find B at point a distance R from the current, just divide by the circumference of the circle which is that distance away.

The magnetic field in space around an electric current is proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source.

To find B at point a distance R from the current, just divide by the circumference of the circle which is that distance away.

The magnetic field in space around an electric current is proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source.

Ampere's Law which is essentially giving the same result of the Biot Savart Law BUT it is simplified because it is useful in situations with a high degree of symmetry like a current in an infinite wire, plane, cylinder, solenoid, etc.

A current produces a circulating magnetic field and the strength of the field can be calculated with the Biot Savart Law OR Ampere's Law (if symmetry exists).

Conclusion of Electrostatics and MagnetoStatics.

There are two parts for both

a) Calculating the Field at any distance from Source

b) Calculating the Force on a test charge or current

Without getting into vector calculus just try to visualize.

1) Electric Fields Radiating from source charges (Coulombs/Gauss' Law).

In this case the Field and Force Laws are the Same

E = Fc/Q where Fc is Coulombs Law

AND

2) Magnetic fields CIRCULATE around currents dictated by the right hand rule (Biot Savart and Ampere's Law).

In this case the Field and Force Laws are different

Field at Any point is calculated from Biot Savart or Ampere's Law

Force is Calculated Using the Lorenz Equation F = qv x B

Putting ALL these equations together you arrive at Maxwell's Equations for Electrostatics and Magnetostatics (more on Maxwell's equations later). Together with the Force Law

F = q(E + v x B) you have all you need to know about electrostatics and magnetostatics.

Charges and Currents are the ONLY sources for ALL electric, magnetic and electromagnetic phenomenon, EVEN in changing electric and magnetic fields as we'll see next. Because PEMF devices using Magnetic fields THAT CHANGE with time, we need to look now at Faradays' Law of Induction.

A current produces a circulating magnetic field and the strength of the field can be calculated with the Biot Savart Law OR Ampere's Law (if symmetry exists).

Conclusion of Electrostatics and MagnetoStatics.

There are two parts for both

a) Calculating the Field at any distance from Source

b) Calculating the Force on a test charge or current

Without getting into vector calculus just try to visualize.

1) Electric Fields Radiating from source charges (Coulombs/Gauss' Law).

In this case the Field and Force Laws are the Same

E = Fc/Q where Fc is Coulombs Law

AND

2) Magnetic fields CIRCULATE around currents dictated by the right hand rule (Biot Savart and Ampere's Law).

In this case the Field and Force Laws are different

Field at Any point is calculated from Biot Savart or Ampere's Law

Force is Calculated Using the Lorenz Equation F = qv x B

Putting ALL these equations together you arrive at Maxwell's Equations for Electrostatics and Magnetostatics (more on Maxwell's equations later). Together with the Force Law

F = q(E + v x B) you have all you need to know about electrostatics and magnetostatics.

Charges and Currents are the ONLY sources for ALL electric, magnetic and electromagnetic phenomenon, EVEN in changing electric and magnetic fields as we'll see next. Because PEMF devices using Magnetic fields THAT CHANGE with time, we need to look now at Faradays' Law of Induction.

**IV. Charges in Motion Part 3 - Time Varying Magnetic Fields (PEMFs) & Magnetic Induction**

**Faradays law**

Remember

Ampere's law: a magnetic (field) can be created by a current. A changing magnetic field can be created from a changing current (what PEMF does).

Faradays law says the reverse: The changing magnetic field can create an electric field and this electric field INDUCES a current. Sometimes for simplicity we just say that a changing magnetic field produces an electric current.

**Technically FARADAYS LAW is a little more subtle, A CHANGING MAGNETIC FIELD INDUCES AN ELECTRIC FIELD (and hence electric currents will flow)**

**Faraday discovered a Changing Magnetic field creates Current in a stationary loop?**

Only electric field or v x B can move a charge.

So if current loop is fixed a changing B creates a current (which Faraday discovered that it did). Something else is moving charges and that is E (because there is no charge or velocity).

What this something else is is a changing magnetic field produces an electric field.

Electric fields up until now were produced by charges, Coulombs force. This new law says that with charges infinitely far away, if I change a magnetic field, I get an electric field. Cannot deduce, must use experiment. That is, a changing Magnetic Field CAN ALSO produce an electric field.

Faradays Law was deduced from Experiment.

To Understand Induction, It helps to look at a Few Experiments

**- Moving a Closed Loop in a Magnetic Field (Lorenz Force, Nothing New)**__Experiment #1__**F**= q(**v**x**B**) - This forces drives the current.__- Keep Loop Stationary, but MOVE THE MAGNET to the left.__

**Experiment #2**SOMETHING NEW - Charges are not moving but there is still a current in the wire!

__- Keep Loop Stationary, and use an electromagnet to DECREASE the magnetic field with time. Here NEITHER the magnet is moving nor the Loop BUT the magnetic field is CHANGING (as it is in ALL 3 Experiements) - That is the common denominator, a CHANGING magnetic field is inducing a current (as we'll see this is Faradays's law of induction. It is a little more subtle than that but this is the simplified jist of it.__

**Experiment #3**In a wire the charges are electrons, in the human body the charges are ions (Ca, Na, K, Cl, Mg, Etc) and proteins... Along with effects of paramagnetic tissues.

It turns out it's not exactly when B changes as B is usually measured on at a point... It is the total amount of magnetic field across the surface of the loop (Called the Magnetic Flux) that changes. Think of wind through a small sail versus a large sail. The flux of air/wind is greater on a larger sail then a smaller sail even though the wind speed is the same. So a larger loop would equate to a large sail to capture more magnetic energy.

Larger current loops in PEMF devices also DELIVER a greater magnetic flux as we've seen with static fields in Biot Savart.

Larger current loops in PEMF devices also DELIVER a greater magnetic flux as we've seen with static fields in Biot Savart.

To sum up, consider two electric circuits next to each other. There will be a magnetic flux through the second circuit due to the current in the first circuit: Ampere's Law. If you change the current in the first circuit, it will change the magnetic flux through the second circuit and the change in magnetic flux will create the current through the second circuit according to Faradays law.

So you see Electricity and Magnetism are related to each other and can be looked upon as two facets of what is called electromagnetism (maybe transition here to Electromagnetic Waves).

Induction in PEMF - PEMF devices uses changing currents to create changing magnetic fields. This can be done by switching the current on and off in very complex ways. The rhythmic switching on and off of an electric current creates pulsating electromagnetic fields. Because they have a time varying frequency, pulsating electromagnetic fields easily produce cell induction (cell membrane ion dissociation) w/o producing cell fatigue. That is , the frequencies and/or amplitudes are dynamic and always changing so the cells do not habituate, or fatigue, to the stimulus. Static magnets produce only one field strength and no frequency. Cells habituate to THAT field strength.

The PEMF device produces a magnetic field that induces currents to flow in nearby tissues. ... (A) In the 1800s, physicians in London discovered that passing an electric current through the fracture site in a broken bone that did not heal properly could jump-start the healing process.

So you see Electricity and Magnetism are related to each other and can be looked upon as two facets of what is called electromagnetism (maybe transition here to Electromagnetic Waves).

Induction in PEMF - PEMF devices uses changing currents to create changing magnetic fields. This can be done by switching the current on and off in very complex ways. The rhythmic switching on and off of an electric current creates pulsating electromagnetic fields. Because they have a time varying frequency, pulsating electromagnetic fields easily produce cell induction (cell membrane ion dissociation) w/o producing cell fatigue. That is , the frequencies and/or amplitudes are dynamic and always changing so the cells do not habituate, or fatigue, to the stimulus. Static magnets produce only one field strength and no frequency. Cells habituate to THAT field strength.

The PEMF device produces a magnetic field that induces currents to flow in nearby tissues. ... (A) In the 1800s, physicians in London discovered that passing an electric current through the fracture site in a broken bone that did not heal properly could jump-start the healing process.

Note: induce is a subtle and slippery verb as it carries a faint odor of causation (produce would make this explicit) without quite committing itself. There is a debate whether a changing magnetic field should be regarded as an independent "source" of electric fields (along with electric charge) - after all the magnetic field ITSELF is do to electric currents.

It is like asking if the postman is the SOURCE of my mail.. Well sure, he delivered it to my door. On the other hand, grandma wrote the letter. Ultimately charge and current are the SOURCES of ALL electromagnetic fields, and a changing magnetic field merely delivers the news from currents elsewhere. But it is often convenient to think of a changing magnetic field "producing" an electric field, and it won't hurt as long as you understand that it is the condensed version of a more complicated story.

It is like asking if the postman is the SOURCE of my mail.. Well sure, he delivered it to my door. On the other hand, grandma wrote the letter. Ultimately charge and current are the SOURCES of ALL electromagnetic fields, and a changing magnetic field merely delivers the news from currents elsewhere. But it is often convenient to think of a changing magnetic field "producing" an electric field, and it won't hurt as long as you understand that it is the condensed version of a more complicated story.

**A Few Examples of Induction**

Lenz's Law adds nothing new to Faradays law it is just a helpful tool to get the direction of the current right.

Lenz's Law in a Nutshell: Nature Abhors a Change in Flux

That is an induced current will flow in such a direction that the flux it produces tends to cancel out the change. Just like when you push on a table it pushes back, you have to push hard enough to get it going. Current is like that too, it takes energy and work to get a current moving from rest (if it didn't we would be violating conservation of energy).

Faraday's law of induction is kind of an inertial phenomenon. A conducing loop likes to maintain a steady current through it. It is hard to get a current going through induction and equally hard to stop or reverse its direction. A current in motion likes to stay in motion.

**(Creating a magnetic field takes energy in the form of getting the current moving - it also stores energy so that when you turn the current OFF you can capture that stored energy (as we'll see).

Lenz's Law in a Nutshell: Nature Abhors a Change in Flux

That is an induced current will flow in such a direction that the flux it produces tends to cancel out the change. Just like when you push on a table it pushes back, you have to push hard enough to get it going. Current is like that too, it takes energy and work to get a current moving from rest (if it didn't we would be violating conservation of energy).

Faraday's law of induction is kind of an inertial phenomenon. A conducing loop likes to maintain a steady current through it. It is hard to get a current going through induction and equally hard to stop or reverse its direction. A current in motion likes to stay in motion.

**(Creating a magnetic field takes energy in the form of getting the current moving - it also stores energy so that when you turn the current OFF you can capture that stored energy (as we'll see).

**Electromotive Force (Voltage or Driving Force in a Circuit)**

There are really two forces involved in driving current around a circuit: the source,

**F,**which is ordinarily confined to one portion of the loop (a battery say), and an electromotive force which serves to smooth out the flow and communicate the influence of the source to distant parts of the circuit.

F (main driving force of the circuit) can be:

- a battery which is a chemical force
- A piezpelectric crystal mechanical pressure converted to an electrical impulse
- A thermocouple where temperature gradient does the work
- A photoelectric cell like solar panels where LIGHT does the job
- Generators of All kinds that where a wire is moved through a magnetic field and a current is INDUCED (electromagnetic induction).

**Human Body**

- a battery which is a chemical force - CELL MEMBRANE/ATP
- A piezpelectric crystal mechanical pressure converted to an electrical impulse (BONES ARE PIEZOELECTRIC and Connective Tissue Matrix is Viscoelectric
- A thermocouple where temperature gradient does the work (Body is Isothermo, so no thermodynamic energy harnessing effects)
- A photoelectric cell like solar panels where LIGHT does the job (Body can capture

light using molecules such as Melanin, Chlorophyll, Hemoglobin, Porphyrine, Billirubin, Cytochromes, Catalases, DNA and more. - Generators of All kinds that where a wire is moved through a magnetic field and a current is INDUCED (electromagnetic induction). Induction - Is used by the Earth's PEMFs and PEMF devices that charge the Cells DIRECTLY. Induction is perhaps THE KEY principle on how PEMF therapy works on the Human body and WHY it penetrates deeper than ANY other form of energy medicine
- Interesting NOTE: when the red blood cells are CHARGED , like a circuit there is an ADDED electrostatic force pushing red blood cells along (like Figure 7.8).

**V. - Maxwells Equations & Electromagnetic Waves (Putting it all together and come FULL CIRCLE).**

**Electromagnetism**is the unified framework to understand electricity, magnetism and the relationship between them.

To understand this relationship first recall that a charge creates an electric field, and the same charge when moving creates a magnetic field.

The electric field exerts an electric force and the magnetic field exerts a magnetic force.

Both originate from electric charge, therefore they are intimately related:

A changing electric field produces a magnetic field and a changing magnetic field produces an electric field.

**Due to this intimacy the two are considered two different manifestations of the same unified force called an Electromagnetic Force or EM force. The unified form of an electric and magnetic field is called an EM field, and the electric and magnetic field are considered its components. In other words, an EM force is exerted by an EM field.**

Where there is a force, there is energy. The energy corresponding to an EM force is called EM energy or radiation. This energy is transferred from one point in space to another through what are called EM waves.

But before we look at the EM Waves lets start with the famous equations which are source of them.

All the principles of electromagnetism can be boiled down to four equations called Maxwells equations.

In the early nineteenth century, when electric and magnetic forces were thought to be two different forces, the physical quantity charge was organized into two different units in electrostatic phenomena and in magnetic phenomenon resulting in two different physical dimensions.

To their surprise, physicists noticed that the ratio of these two different units had the unit of velocity and it was precisely the speed of light! At the time no one could explain this.

In the early nineteenth century, when electric and magnetic forces were thought to be two different forces, the physical quantity charge was organized into two different units in electrostatic phenomena and in magnetic phenomenon resulting in two different physical dimensions.

To their surprise, physicists noticed that the ratio of these two different units had the unit of velocity and it was precisely the speed of light! At the time no one could explain this.

When electric and magnetic fields do not vary with time we can analyze them independent of one another. However when they DO vary with time, they are interrelated.

For example Faraday's law states that a magnetic field varying with time generates an electric field (induced currents in inductors and transformers).

In reverse, Ampere's law states that an electric current or an electric field varying with time generates a magnetic field.

James Clerk Maxwell put all this together when in 1865 he showed that an EM disturbance (wave) would propagate in space at the speed of light, and hence LIGHT was a wave (classically) and was electromagnetic in nature. Maxwell realized the basic principles of electromagnetism can be expressed in terms of four equations which display the mutual interaction between electric and magnetic fields.

For example Faraday's law states that a magnetic field varying with time generates an electric field (induced currents in inductors and transformers).

In reverse, Ampere's law states that an electric current or an electric field varying with time generates a magnetic field.

James Clerk Maxwell put all this together when in 1865 he showed that an EM disturbance (wave) would propagate in space at the speed of light, and hence LIGHT was a wave (classically) and was electromagnetic in nature. Maxwell realized the basic principles of electromagnetism can be expressed in terms of four equations which display the mutual interaction between electric and magnetic fields.

To start from the top of the chart above, the integtal forms of the first two Maxwell' equations involve the integrals of the electric and magnetic fields over a closed surface.

These two equations are Gauss's law for electricity and magnetism.

Shows how static charge creates a radiating electric field such that the total flux (surface integral) is equal to the inclosed charge divided by constant eo.

These two equations are Gauss's law for electricity and magnetism.

Shows how static charge creates a radiating electric field such that the total flux (surface integral) is equal to the inclosed charge divided by constant eo.

**Divergence - 1st two Maxwells (Gauss's Law for Electricity and Magnetism**

First 2 Maxwell equations how radiating electric fields and magnetic fields created.

Divergence is well chosen for it is a measure of how much the field spreads out from a point in question. Positive divergence flows OUT like a faucet/source, while negative divergence flows IN like a drain/sink.

+ positive Electric charge is the Source for the electric field - Field Lines Flow out

- negative Electric charge is the Sink for the electric field - Field Lines Flow IN

Note: there are NO magnetic monopoles or SOURCE charges for the magnetic field which is why the second equation is = 0.

Divergence is PARTICLE - LIKE

The third equation is Faradays law of of EM induction which shows how a time varying magnetic field generates a CIRCULATING electric field.

And the 4th and last Maxwell equation expresses Amperes law by showing how an electric current can generate a magnetic field PLUS the second term in the equation was added by Maxwell (not in Ampere's original equation) in analogy with Faradays law, to account for the fact that a time varying electric field also generates a circulating magnetic field....

WHICH than in turn creates a time varying electric field... (leads to 3D wave equations describing EM waves).

And the 4th and last Maxwell equation expresses Amperes law by showing how an electric current can generate a magnetic field PLUS the second term in the equation was added by Maxwell (not in Ampere's original equation) in analogy with Faradays law, to account for the fact that a time varying electric field also generates a circulating magnetic field....

**A Changing Electric Field induces a magnetic field (something Faraday had to ADD to Ampere's law to account for CHANGING currents (like PEMF therapy!!).**

ADD TO This Faradays' Law that a Changing Magnetic Field Induces an Electric field and you HAD the basis for how EM waves propagate in space (as we'll see).ADD TO This Faradays' Law that a Changing Magnetic Field Induces an Electric field and you HAD the basis for how EM waves propagate in space (as we'll see).

WHICH than in turn creates a time varying electric field... (leads to 3D wave equations describing EM waves).

**Curl - 2nd Two Maxwells (Faradays Law of Induction and Ampere's law of Current Flow)**

Last Two equations how circulating electric and magnetic fields are created.

AND how changing electric and magnetic fields create each other (leads to EM waves)

The name curl is ALSO well chosen, for it is a measure of how much a field swirls around the point in question. Use the right hand rule for detecting POSITIVE curl (counterclockwise) and negative curl (counterclockwise).

CURL IS WAVELIKE

Maxwell's Equations in differential form

These Four Equations TOGETHER with the Force Law

Summarize the ENTIRETY of Classical Electrodynamics (not including Relativity and Quantum Electrodynamics).

Writing Maxwell's equations Like above in what is called differential form, emphasizes that they specify the divergence and curl of E and B.

In THIS form, they reinforce the notion that electric fields can be produced EITHER by CHARGES (particles) OR by changing magnetic Fields (waves),

AND magnetic fields can be produced either by currents/moving charges (particles) OR changing electric fields (waves).

But ultimately ALL fields come from charges and currents (moving charges) or that is Charges.

Maxwell's equations really show how charges (stationary or moving)/particles produce FIELDS (waves)!!

The Force Law reciprocally tells you how FIELDS (waves) affect charges (particles)!

Now in the absence of charges and currents, we find Electric and Magnetic fields can continuously reinforce and propagate one another. The WAVE equations come from setting the charge and current = 0.

These Four Equations TOGETHER with the Force Law

**F**= q(**E**+**v**x**B**)Summarize the ENTIRETY of Classical Electrodynamics (not including Relativity and Quantum Electrodynamics).

Writing Maxwell's equations Like above in what is called differential form, emphasizes that they specify the divergence and curl of E and B.

In THIS form, they reinforce the notion that electric fields can be produced EITHER by CHARGES (particles) OR by changing magnetic Fields (waves),

AND magnetic fields can be produced either by currents/moving charges (particles) OR changing electric fields (waves).

But ultimately ALL fields come from charges and currents (moving charges) or that is Charges.

Maxwell's equations really show how charges (stationary or moving)/particles produce FIELDS (waves)!!

The Force Law reciprocally tells you how FIELDS (waves) affect charges (particles)!

Now in the absence of charges and currents, we find Electric and Magnetic fields can continuously reinforce and propagate one another. The WAVE equations come from setting the charge and current = 0.

In the Absence of charges and currents, Maxwells equations can be transformed into the the following 3D wave equations. Compare below to previous Maxwell's equations. All we have done is set p and J to zero (charge density and current density). So in free space WAVES CAN propagate because a changing electric field creates a changing magnetic field and in turn a changing magnetic field creates an electric field.

The equations above constitute a set of coupled first order differential equations for E and B. They can be decoupled by applying the curl to both equations on the right.

Now we have separate equations for E and B, but they are second order, which is the price you pay for decoupling them (this has to do with each E and B changing create each other (1st order), and how E and B change themselves in second order because its change of a change...

E -> B -> E -> B (first order)

E ->(B) -> E -> -> E (second order)

In a vacuum, each of the Cartesian Components of E and B satisfies the 3 dimensional wave equation traveling a speed v = 1/ root(eo*uo) ... SEE BELOW

The equations above constitute a set of coupled first order differential equations for E and B. They can be decoupled by applying the curl to both equations on the right.

Now we have separate equations for E and B, but they are second order, which is the price you pay for decoupling them (this has to do with each E and B changing create each other (1st order), and how E and B change themselves in second order because its change of a change...

E -> B -> E -> B (first order)

E ->(B) -> E -> -> E (second order)

In a vacuum, each of the Cartesian Components of E and B satisfies the 3 dimensional wave equation traveling a speed v = 1/ root(eo*uo) ... SEE BELOW

The implication is astounding: Perhaps LIGHT is an electromagnetic wave. Of course the conclusion does not surprise anyone today, but imagine the revelation in Maxwell's time!!

eo and uo came into the theory as constants in Coulombs Law and the Biot Savart Law respectively. You measure them in experiments with pith balls, batteries and wires - experiments which have NOTHING to do with light. And yet, according to Maxwell's theory, you calculate c, the speed of light from these two numbers.

We won't derive further equations for electromagnetic waves because it gets a little hairy in 3 dimensions. But the principles are essential similar to our simple 1D wave we discussed early. But the simplest ones are monochromatic (1 frequency sinusoidal) plane waves. But you have to think now in terms of a point source and a wave spreading in all directions. The 2 D version of this is like a pebble in a pond (with only one frequency).

Can you stretch your mind to see this in 3D?

eo and uo came into the theory as constants in Coulombs Law and the Biot Savart Law respectively. You measure them in experiments with pith balls, batteries and wires - experiments which have NOTHING to do with light. And yet, according to Maxwell's theory, you calculate c, the speed of light from these two numbers.

We won't derive further equations for electromagnetic waves because it gets a little hairy in 3 dimensions. But the principles are essential similar to our simple 1D wave we discussed early. But the simplest ones are monochromatic (1 frequency sinusoidal) plane waves. But you have to think now in terms of a point source and a wave spreading in all directions. The 2 D version of this is like a pebble in a pond (with only one frequency).

Can you stretch your mind to see this in 3D?

So what is the frequency of EM waves?

Electromagnetic waves cover a wide spectrum of frequencies and the ranges of these frequencies is one way to define different types of EM waves.

Recall a wave transfers energy from one point to another in space.

Disturbance that defines the wave and

the propagation of the wave.

EM waves are traverse waves which means that the electric and magnetic fields change or oscillate in a plane that is perpendicular to the direction of propagation (and also note the electric and magnetic field in an EM wave are perpendicular to each other.

Electromagnetic waves cover a wide spectrum of frequencies and the ranges of these frequencies is one way to define different types of EM waves.

Recall a wave transfers energy from one point to another in space.

Disturbance that defines the wave and

the propagation of the wave.

EM waves are traverse waves which means that the electric and magnetic fields change or oscillate in a plane that is perpendicular to the direction of propagation (and also note the electric and magnetic field in an EM wave are perpendicular to each other.

Because electric and magnetic fields change in a plane that is perpendicular to direction of wave propagation, the direction of change still has some freedom... Linearly and circularly polarized.

**Below is the Full Range of the Electromagnetic Spectrum.**

Visible like is an example of EM waves as is gamma, x-ray, UV, IR, microwave and radio waves all of which can be further broken down into subgroups. All these classifications are based on FREQUENCY!!

Some 73 Octaves of Frequencies from low ELF to Gamma Rays.

Visible Light is only a Narrow Sliver in this Vast Spectrum!!

But it turns out to be the PEAK output of our Sun, showing how our eyes and life adapts to Nature.

We have come FULL circle and completed the cycle. This whole video is one big wave that repeated itself.

OK , now it is time to WAVE goodbye!!

OK , now it is time to WAVE goodbye!!

Bioelectromagnetism and biomagnetism are the study of the production of electromagnetic and magnetic fields by biological organisms.

The sensing of magnetic fields by organisms is known as magnetoreception.

Magnetobiology is a subset of bioelectromagnetics.

Biological effects of weak low frequency magnetic fields, less than about 0.1 millitesla (or 1 Gauss) and 100 Hz correspondingly, constitutes a physics problem. The effects look paradoxical, for the energy quantum of these electromagnetic fields is by many orders of value less than the energy scale of an elementary chemical act. On the other hand, the field intensity is not enough to cause any appreciable heating of biological tissues or irritate nerves by the induced electric currents.

BUT as research has shown low frequency and low intensity PEMF has thousands of published research studies showing many positive effects on the human body.

The sensing of magnetic fields by organisms is known as magnetoreception.

**Magnetobiology studies magnetic fields as a medical treatment; namely weak and low frequency magnetic fields**

Naturally produced by an organism are known as biomagnetism (also low frequency and weak intensity).Naturally produced by an organism are known as biomagnetism (also low frequency and weak intensity).

Magnetobiology is a subset of bioelectromagnetics.

Biological effects of weak low frequency magnetic fields, less than about 0.1 millitesla (or 1 Gauss) and 100 Hz correspondingly, constitutes a physics problem. The effects look paradoxical, for the energy quantum of these electromagnetic fields is by many orders of value less than the energy scale of an elementary chemical act. On the other hand, the field intensity is not enough to cause any appreciable heating of biological tissues or irritate nerves by the induced electric currents.

BUT as research has shown low frequency and low intensity PEMF has thousands of published research studies showing many positive effects on the human body.

**Inducing Current from One Loop to another...**

Mutual Inductance - Only depends on Geometry and shape (not intensity).

It is kinda an astonishing Conclusion: Whatever the shapes and positions of the loops, the flux through 2 when we run a current through 1, is IDENTICAL to the flux through 1 when we run a current through 2.

In PEMF envision that the source coil is inducing CURRENTS in the BODY CIRCUIT of charged ions, proteins, etc.

**Self Inductance**

A changing current not only induces an emf in any nearby loop, it also induces an emf in the source loop itself. And once again the field (and therefore the flux) is proportional to the current.

Inductance is an intrinsically positive quantity. Lenz's law whcih is enforced by the minus sign dictates that the emf is in such a direction as to oppose any change in current. For this reason it is called a BACK EMF. Whenever you try to alter the current in a wire, you must fight against this back EMF. Inductance plays a similar role in electric circuits as mass plays in mechanical systems:

**The LARGER THE L (Inductance) is, the harder it is to change the current (electric energy), just as the larger the mass, the harder it is to change an objects velocity (kinetic energy).**

**Energy Stored in a Magnetic Field**

It takes a certain amount of energy to get a current going in a circuit. The work done is against the back EMF and it is Recoverable unlike the heat lost in a resistor.

U = 1/2LI^2

(U is the energy, L the inductance and I is the current).

It does not depend on how long we take to crank up the current, only on the geometry of the loop (in the Form of L) and the final current I.

Another way to look at it is that the energy is STORED in the field itself in the amount U = B^2/2uo.

**So you can look at the energy in two ways**

**1)**The energy is stored in the current distribution (particle - electron)

**2)**The energy is stored in the field itself. (wave - field)

The distinction is one of bookkeeping, as the important quantity is the total energy.

So it takes ENERGY to set up a magnetic field even though magnetic fields do not work. BUT changing magnetic fields induces Electric fields WHICH DO WORK.

So take a current from ZERO to the final current is taking the Magnetic field from Zero to the final Field level ... It is this CHANGE in current (or Change in B) that does work in the form a changing electric field.

Amperes Law is that a current creates a magnetic field.

__As we'll see__ALSO a Changing Electric Field induces a magnetic field (something Faraday had to ADD to Ampere's law to account for CHANGING currents (like PEMF therapy!!).Faradays Law is a Changing Magnetic field induces an electric field and hence can create current.

Most energy medicine devices are electromagnetic in nature deal with the last 3 types of energy which are all manifestations of the Electromagnetic Force.

The tricky part comes when you try to think about the forces between magnets and charged particles. Magnetic forces on charged particles are a new kind of beast called velocity dependent forces.

***Electrostatic energy**is just another word for the potential energy associated with the forces of attraction and repulsion between electrically charged particles. Along with gravitational energy it is the primary form of potential energy in the ordinary classical world.***Currents and Micro-currents*****Magnetic energy**is tricky, but the force between the poles of magnets is a form of potential energy.The tricky part comes when you try to think about the forces between magnets and charged particles. Magnetic forces on charged particles are a new kind of beast called velocity dependent forces.

***Energy stored in electromagnetic radiation**. Heat or light from the sun or the energy stored in radio waves, laser light or other forms of radiation… In some very general sense it is a combination of kinetic and potential energy, but it is NOT the energy of particles for of fields.. needs quantum field theory to properly understand.

**Optional - More Precise Definition of a wave**A wave is a disturbance of a continuous medium that propagates with a fixed shape at a constant velocity.

**Main points of a wave are its

**fixed shaped and constant speed**

ALSO for completeness

- In the presence of absorption, the wave will diminish in size as it moves.

- If the medium is dispersive, different frequencies travel at different speeds (think prism).

- In two or three dimensions, the

**wave spreads out, it's amplitude (or intensity) will decrease.**

- Standing waves do not propagate at all (Schumann Resonance creates quasi- standing waves (never perfect because ionosphere to earth geometry is always changing. But in essence it is close).

**BACK TO THE WATER ANALOGY**

Just use to get an intuitive FEEL for the concepts and fluid flow through pipes is a little easier to visualize than current flow in circuits.