I. Electrostatics - Charges at Rest
Electric Charge, Coulombs Law & Gauss's Law
Electric Charge, Coulombs Law & Gauss's Law
Electromagnetism (Electricity, Magnetism and Electromagnetic Waves)
To Understand Electromagnetic Waves and PEMF Therapy, it is important to understand Electricity and Magnetism.
Most of you have a direct experience with electric charge. Really try to get an intuitive understanding of charge because EVERYTHING in electromagnetism (light included) comes from static, moving or accelerating charges.
To Understand Electromagnetic Waves and PEMF Therapy, it is important to understand Electricity and Magnetism.
Most of you have a direct experience with electric charge. Really try to get an intuitive understanding of charge because EVERYTHING in electromagnetism (light included) comes from static, moving or accelerating charges.
I. Electrostatics - Charges at Rest
Force of Electrostatics...
Perhaps you have walked across a carpet on a dry day and reached out your hand to touch door knob and received a small shock, or when separating your bed covers at night you've heard a crackle and seen the light glowing under from under you covers as you pull them off. Electricity is the property of some particles of matter related to electric charge.
Force of Electrostatics...
Perhaps you have walked across a carpet on a dry day and reached out your hand to touch door knob and received a small shock, or when separating your bed covers at night you've heard a crackle and seen the light glowing under from under you covers as you pull them off. Electricity is the property of some particles of matter related to electric charge.
Who Discovered Electricity?
Electricity is a form of energy and it occurs in nature, so it was not “invented.” As to who discovered it, many misconceptions abound. Some give credit to Benjamin Franklin for discovering electricity, but his experiments only helped establish the connection between lightning and electricity, nothing more.
The truth about the discovery of electricity is a bit more complex than a man flying his kite. It actually goes back more than two thousand years.
Electricity is a form of energy and it occurs in nature, so it was not “invented.” As to who discovered it, many misconceptions abound. Some give credit to Benjamin Franklin for discovering electricity, but his experiments only helped establish the connection between lightning and electricity, nothing more.
The truth about the discovery of electricity is a bit more complex than a man flying his kite. It actually goes back more than two thousand years.
From ancient times, people were familiar with different types of phenomena that today would all be explained using the concept of electric charge:
(a) lightning,
(b) the torpedo fish (or electric ray),
(c) St Elmo's Fire, and
(d) that amber rubbed with fur would attract small, light objects.
It has been recorded that Thales of Miletus around 640 B.C. rubbed amber (which is fossilized tree sap) and discovered it would attract leaves.
THAY:leez of mi:LAY:tus
In fact the word electron comes from the Greek or Latin word for Amber.
(a) lightning,
(b) the torpedo fish (or electric ray),
(c) St Elmo's Fire, and
(d) that amber rubbed with fur would attract small, light objects.
It has been recorded that Thales of Miletus around 640 B.C. rubbed amber (which is fossilized tree sap) and discovered it would attract leaves.
THAY:leez of mi:LAY:tus
In fact the word electron comes from the Greek or Latin word for Amber.
Additionally, researchers and archeologists in the 1930’s discovered pots with sheets of copper inside that they believe may have been ancient batteries meant to produce light at ancient Roman sites. Similar devices were found in archeological digs near Baghdad meaning ancient Persians may have also used an early form of batteries.
In the year 1600, English physician William Gilbert used the Latin word “electricus” to describe the force that certain substances exert when rubbed against each other. A few years later another English scientist, Thomas Browne, wrote several books and he used the word “electricity” to describe his investigations based on Gilbert’s work.
In 1752, Ben Franklin conducted his experiment with a kite, a key, and a storm. This simply proved that lightning and tiny electric sparks were the same thing.
Italian physicist Alessandro Volta discovered that particular chemical reactions could produce electricity, and in 1800 he constructed the voltaic pile (an early electric battery) that produced a steady electric current.
We will pick up the history of electricity through this course with inventions and discoveries by Ampere, by Faraday, Edison, Tesla, and more.
While the concept of electricity was known for thousands of years, when it came time to develop it commercially and scientifically, there were several great minds working on the problem at the same time.
In the year 1600, English physician William Gilbert used the Latin word “electricus” to describe the force that certain substances exert when rubbed against each other. A few years later another English scientist, Thomas Browne, wrote several books and he used the word “electricity” to describe his investigations based on Gilbert’s work.
In 1752, Ben Franklin conducted his experiment with a kite, a key, and a storm. This simply proved that lightning and tiny electric sparks were the same thing.
Italian physicist Alessandro Volta discovered that particular chemical reactions could produce electricity, and in 1800 he constructed the voltaic pile (an early electric battery) that produced a steady electric current.
We will pick up the history of electricity through this course with inventions and discoveries by Ampere, by Faraday, Edison, Tesla, and more.
While the concept of electricity was known for thousands of years, when it came time to develop it commercially and scientifically, there were several great minds working on the problem at the same time.
Though he didn’t discover electricity, Benjamin Franklin coined most of the words we use today to describe it, including battery, conductor, and positive and negative charges.
Did Franklin actually test his theories by flying a kite in a thunderstorm? No one is sure.
In no version of the story, however, was Franklin's kite actually struck by lightning. That would have resulted in chicken-fried Franklin [source: MythBusters]. Instead, when a storm approached, Franklin noticed the hairs on the kite string standing up, indicating the presence of electricity in the air. When he touched the key tied to the string, it released a nice spark, sealing the deal.
When Benjamin Franklin demonstrated that lightning was related to static electricity. Static electricity is just one aspect of the electromagnetic force, which also includes moving electricity and magnetism and light.
All the macroscopic forces that we experience directly, such as the sensations of touch, taste, vision are due to the electromagnetic force, one of the four fundamental forces in nature. The gravitational force, another fundamental force, is actually sensed through the electromagnetic interaction of molecules, such as between those in our feet and those on the top of a bathroom scale. (The other two fundamental forces, the strong nuclear force and the weak nuclear force, cannot be sensed on the human scale.) Because of electromagnetic interactions, really nothing is touching, its the strong electromagnetic force at play. Interestingly we literally levitate off the ground but only by
We truly feel and sense the world around us because of Electromagnetism!!
Did Franklin actually test his theories by flying a kite in a thunderstorm? No one is sure.
In no version of the story, however, was Franklin's kite actually struck by lightning. That would have resulted in chicken-fried Franklin [source: MythBusters]. Instead, when a storm approached, Franklin noticed the hairs on the kite string standing up, indicating the presence of electricity in the air. When he touched the key tied to the string, it released a nice spark, sealing the deal.
When Benjamin Franklin demonstrated that lightning was related to static electricity. Static electricity is just one aspect of the electromagnetic force, which also includes moving electricity and magnetism and light.
All the macroscopic forces that we experience directly, such as the sensations of touch, taste, vision are due to the electromagnetic force, one of the four fundamental forces in nature. The gravitational force, another fundamental force, is actually sensed through the electromagnetic interaction of molecules, such as between those in our feet and those on the top of a bathroom scale. (The other two fundamental forces, the strong nuclear force and the weak nuclear force, cannot be sensed on the human scale.) Because of electromagnetic interactions, really nothing is touching, its the strong electromagnetic force at play. Interestingly we literally levitate off the ground but only by
We truly feel and sense the world around us because of Electromagnetism!!
Franklin wrote in his letters and books that he could see the effects of electric charge but did not understand what caused the phenomenon.
Today we know that electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
There are two types of electric charges; positive and negative (commonly carried by protons and electrons respectively).
Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral.
By some strange convention, electrons were given this minus sign by Benjamin Franklin.
This figure shows a simple model of an atom with negative electrons orbiting its positive nucleus. The nucleus is positive due to the presence of positively charged protons. Nearly all charge in nature is due to electrons and protons, which are two of the three building blocks of most matter. (The third is the neutron, which is neutral, carrying no charge.) Other charge-carrying particles are observed in cosmic rays and nuclear decay, and are created in particle accelerators. All but the electron and proton survive only a short time and are quite rare by comparison.
An interesting fact is protons and electrons seem to be by particle standards more or less immortal (Scientists are still looking for proton decay and still never has been found). All other fundamental particles decay!
There are two types of electric charges; positive and negative (commonly carried by protons and electrons respectively).
Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral.
By some strange convention, electrons were given this minus sign by Benjamin Franklin.
This figure shows a simple model of an atom with negative electrons orbiting its positive nucleus. The nucleus is positive due to the presence of positively charged protons. Nearly all charge in nature is due to electrons and protons, which are two of the three building blocks of most matter. (The third is the neutron, which is neutral, carrying no charge.) Other charge-carrying particles are observed in cosmic rays and nuclear decay, and are created in particle accelerators. All but the electron and proton survive only a short time and are quite rare by comparison.
An interesting fact is protons and electrons seem to be by particle standards more or less immortal (Scientists are still looking for proton decay and still never has been found). All other fundamental particles decay!
NOTE: No protons have radioactively decayed after decades of searching, leaving the beloved theory of grand unification in limbo.) Also Combining conservation of energy with conservation of electric charge tells us that electrons are probably stable forever
NOTE2: A free neutron is unstable, decaying to a proton, electron and antineutrino with a mean lifetime of just under 15 minutes (881.5±1.5 s). This radioactive decay, known as beta decay, is possible because the mass of the neutron is slightly greater than the proton.
The Super-Kamiokande observatory pictured here in Kamioka, Japan, has never found a proton decay (nor has any other laboratory as of 4/3/19)!
NOTE2: A free neutron is unstable, decaying to a proton, electron and antineutrino with a mean lifetime of just under 15 minutes (881.5±1.5 s). This radioactive decay, known as beta decay, is possible because the mass of the neutron is slightly greater than the proton.
The Super-Kamiokande observatory pictured here in Kamioka, Japan, has never found a proton decay (nor has any other laboratory as of 4/3/19)!
The first interesting thing is that every electron anywhere in the universe has exactly the same charge. It also has exactly the same mass. But at the microscopic level of electrons and protons, every electron and every proton anywhere in the universe is identical. I find that fascinating.
There's an idea that suggests all the universe's electrons are actually one particle forever traveling backwards and forwards in time. It's a simple, elegant idea that solves some of physics's biggest mysteries. There's only one tiny problem. It's complete nonsense.
This is the story of that bizarre thought experiment and John Archibald Wheeler, the brilliant, largely unsung physicist who came up with it.
There's an idea that suggests all the universe's electrons are actually one particle forever traveling backwards and forwards in time. It's a simple, elegant idea that solves some of physics's biggest mysteries. There's only one tiny problem. It's complete nonsense.
This is the story of that bizarre thought experiment and John Archibald Wheeler, the brilliant, largely unsung physicist who came up with it.
The One Electron Universe - Thought Experiment. Very Interesting Aside...
The one electron universe is, among other things, one of the very few attempts to explain why all electrons are identical. It has its roots in an entirely different form of symmetry between particles, that of an electron and its antimatter counterpart, the positron. The two particles have the same mass, the same spin, the same everything except for its charge. Leaving the charge aside, the electron and the positron are, well, indistinguishable, and in 1940 that gave a Princeton physicist named John Wheeler an idea.
https://io9.gizmodo.com/what-if-every-electron-in-the-universe-was-all-the-same-5876966
Check out this interesting article for more on the one electron Universe.
The one electron universe is, among other things, one of the very few attempts to explain why all electrons are identical. It has its roots in an entirely different form of symmetry between particles, that of an electron and its antimatter counterpart, the positron. The two particles have the same mass, the same spin, the same everything except for its charge. Leaving the charge aside, the electron and the positron are, well, indistinguishable, and in 1940 that gave a Princeton physicist named John Wheeler an idea.
https://io9.gizmodo.com/what-if-every-electron-in-the-universe-was-all-the-same-5876966
Check out this interesting article for more on the one electron Universe.
Secondly charge is conserved. Conserved is a physics terms for saying — does not change with time or charge cannot be created or destroyed.
LAW OF CONSERVATION OF CHARGE
Total charge is constant in any process.
No charge is actually created or destroyed when charges are separated as we have been discussing. Rather, existing charges are moved about. In fact, in all situations the total amount of charge is always constant. This universally obeyed law of nature is called the law of conservation of charge.
LAW OF CONSERVATION OF CHARGE
Total charge is constant in any process.
No charge is actually created or destroyed when charges are separated as we have been discussing. Rather, existing charges are moved about. In fact, in all situations the total amount of charge is always constant. This universally obeyed law of nature is called the law of conservation of charge.
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Thirdly, Charge is quantized (that is charge is granular not continuous); it comes in integer multiples of individual small units called the elementary charge, e, about 1.602×10−19 coulombs, which is the smallest charge which can exist free (particles called quarks have smaller charges, multiples of 1/3 e, but they are only found in combination, and always combine to form particles with integer charge). The proton has a charge of +e, and the electron has a charge of −e.
Interestingly even though protons weight approximately 1800x electrons, their charges are identical.
Interestingly even though protons weight approximately 1800x electrons, their charges are identical.
The electron seems to have no substructure; in contrast, when the substructure of protons is explored by scattering extremely energetic electrons from them, it appears that there are point-like particles inside the proton.
These sub-particles, named quarks, have never been directly observed, but they are believed to carry fractional charges as seen in this Figure. Charges on electrons and protons and all other directly observable particles are unitary, but these quark substructures carry charges of either +2/3 or -1/3.
There are continuing attempts to observe fractional charge directly and to learn of the properties of quarks, which are perhaps the ultimate substructure of matter.
These sub-particles, named quarks, have never been directly observed, but they are believed to carry fractional charges as seen in this Figure. Charges on electrons and protons and all other directly observable particles are unitary, but these quark substructures carry charges of either +2/3 or -1/3.
There are continuing attempts to observe fractional charge directly and to learn of the properties of quarks, which are perhaps the ultimate substructure of matter.
In more exotic situations, such as in particle accelerators, mass, Δm, can be created from energy in the amount Change M = E/c^2
Sometimes, the created mass is charged, such as when an electron is created. Whenever a charged particle is created, another having an opposite charge is always created along with it, so that the total charge created is zero. Usually, the two particles are “matter-antimatter” counterparts. For example, an antielectron would usually be created at the same time as an electron. The antielectron has a positive charge (it is called a positron), and so the total charge created is zero. (See Figure) All particles have antimatter counterparts with opposite signs. When matter and antimatter counterparts are brought together, they completely annihilate one another. By annihilate, we mean that the mass of the two particles is converted to energy E, again obeying the relationship Change M = E/c^2
Since the two particles have equal and opposite charge, the total charge is zero before and after the annihilation; thus, total charge is conserved.
Sometimes, the created mass is charged, such as when an electron is created. Whenever a charged particle is created, another having an opposite charge is always created along with it, so that the total charge created is zero. Usually, the two particles are “matter-antimatter” counterparts. For example, an antielectron would usually be created at the same time as an electron. The antielectron has a positive charge (it is called a positron), and so the total charge created is zero. (See Figure) All particles have antimatter counterparts with opposite signs. When matter and antimatter counterparts are brought together, they completely annihilate one another. By annihilate, we mean that the mass of the two particles is converted to energy E, again obeying the relationship Change M = E/c^2
Since the two particles have equal and opposite charge, the total charge is zero before and after the annihilation; thus, total charge is conserved.
Electrostatic Force
Here is a little experiment you can do to illustrate the Electrostatic Force that is illustrated in this short video clip.
Take a plastic comb and some little pieces of paper.
Comb your hair nice and good and then hold the comb over the paper.
The paper "Jumps" up to the comb if the comb is a reasonable distance away.
Now that might seem like no big deal, BUT, the electrostatic force of electrons on a little comb TRIUMPHS over the gravitational force of the ENTIRE MASS OF THE EARTH!!!!
The reason for this is the electromagnetic force is more than a trillion trillion trillion 10^36 times stronger than gravity. The reason Gravity WINS cosmically on the large scale is because most things are electrically neutral.
Yes. Most things are electrically neutral. In other words, electric force, even though it’s very strong, comes with opposite charges. It can occur with a plus sign or with a minus sign. Therefore, if you take the planet Earth, it’s got lots and lots of charges in every atom, but every atom is neutral.
Here is a little experiment you can do to illustrate the Electrostatic Force that is illustrated in this short video clip.
Take a plastic comb and some little pieces of paper.
Comb your hair nice and good and then hold the comb over the paper.
The paper "Jumps" up to the comb if the comb is a reasonable distance away.
Now that might seem like no big deal, BUT, the electrostatic force of electrons on a little comb TRIUMPHS over the gravitational force of the ENTIRE MASS OF THE EARTH!!!!
The reason for this is the electromagnetic force is more than a trillion trillion trillion 10^36 times stronger than gravity. The reason Gravity WINS cosmically on the large scale is because most things are electrically neutral.
Yes. Most things are electrically neutral. In other words, electric force, even though it’s very strong, comes with opposite charges. It can occur with a plus sign or with a minus sign. Therefore, if you take the planet Earth, it’s got lots and lots of charges in every atom, but every atom is neutral.
Interesting ASIDE:
You Can Never Actually Touch Anything (according to Physics)
If you’re reading this right now, it’s a sure bet that you are touching something, be it your keyboard, mouse, cellphone, laptop, chair, desk, or a nice plush bed with 1500 thread count Egyptian-cotton sheets.
Speaking of that nice plush, comfy bed, I hate to shatter the illusion, but you aren’t actually touching it.
Particles are, by their very nature, attracted to particles with an opposite charge, and they repel other similarly charged particles.
This prevents electrons from ever coming in direct contact (in an atomic sense and literal sense). Their wave packets, on the other hand, can overlap, but never touch.
The same is true for all of humankind. When you plop down in a chair or slink into your bed, the electrons within your body are repelling the electrons that make up the chair. You are hovering above it by an unfathomably small distance. We literally leviate and hover through life, but only by about 10^-8 meters!!
You Can Never Actually Touch Anything (according to Physics)
If you’re reading this right now, it’s a sure bet that you are touching something, be it your keyboard, mouse, cellphone, laptop, chair, desk, or a nice plush bed with 1500 thread count Egyptian-cotton sheets.
Speaking of that nice plush, comfy bed, I hate to shatter the illusion, but you aren’t actually touching it.
Particles are, by their very nature, attracted to particles with an opposite charge, and they repel other similarly charged particles.
This prevents electrons from ever coming in direct contact (in an atomic sense and literal sense). Their wave packets, on the other hand, can overlap, but never touch.
The same is true for all of humankind. When you plop down in a chair or slink into your bed, the electrons within your body are repelling the electrons that make up the chair. You are hovering above it by an unfathomably small distance. We literally leviate and hover through life, but only by about 10^-8 meters!!
Through the work of scientists in the late 18th century, the main features of the electrostatic force—the existence of two types of charge, the observation that like charges repel, unlike charges attract, and the decrease of force with distance—were eventually refined, and expressed as a mathematical formula. The mathematical formula for the electrostatic force is called Coulomb’s law after the French physicist Charles Coulomb (1736–1806), who performed experiments and first proposed a formula to calculate it.
Coulomb's law is an exact formula derived from experiment that allows us to calculate the Electrostatic Force between 2 or more charged particles (superposition).
Modern experiments have verified Coulomb’s law to great precision. For example, it has been shown that the force is inversely proportional to distance between two objects squaredto an accuracy of 1 part in 10^16. No exceptions have ever been found, even at the small distances within the atom.
The force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The constant of proportionality k = 1/4pi*eo.
eo is the electric permittivity constant in free space and is a measure of how much a vacuum in space shields the electric charge (we'll come back to this later and ultimately see how it is tied to the speed of light!).
It looks a lot like the gravitational force between two point masses except the we multiply charge instead of mass and the constant is different. But they are both inverse square laws.
It is actually much more practical to work with the field formulation using the electric field. The reason is that whereas q1 and q2 exist only at these two places, the electric field can be defined everywhere as we'll see.
Coulomb's law is an exact formula derived from experiment that allows us to calculate the Electrostatic Force between 2 or more charged particles (superposition).
Modern experiments have verified Coulomb’s law to great precision. For example, it has been shown that the force is inversely proportional to distance between two objects squaredto an accuracy of 1 part in 10^16. No exceptions have ever been found, even at the small distances within the atom.
The force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The constant of proportionality k = 1/4pi*eo.
eo is the electric permittivity constant in free space and is a measure of how much a vacuum in space shields the electric charge (we'll come back to this later and ultimately see how it is tied to the speed of light!).
It looks a lot like the gravitational force between two point masses except the we multiply charge instead of mass and the constant is different. But they are both inverse square laws.
It is actually much more practical to work with the field formulation using the electric field. The reason is that whereas q1 and q2 exist only at these two places, the electric field can be defined everywhere as we'll see.
Aside: Electrostatics and DNA
DNA is a highly charged molecule. The DNA double helix shows the two coiled strands each containing a row of nitrogenous bases, which “code” the genetic information needed by a living organism. The strands are connected by bonds between pairs of bases. While pairing combinations between certain bases are fixed (C-G and A-T), the sequence of nucleotides in the strand varies.
Since the Coulomb force drops with distance the distances between the base pairs must be small enough that the electrostatic force is sufficient to hold them together.
DNA is a highly charged molecule, with about 2qe (fundamental charge) per 0.3 × 10^−9 m. The distance separating the two strands that make up the DNA structure is about 1 nm, while the distance separating the individual atoms within each base is about 0.3 nm.
DNA is a highly charged molecule. The DNA double helix shows the two coiled strands each containing a row of nitrogenous bases, which “code” the genetic information needed by a living organism. The strands are connected by bonds between pairs of bases. While pairing combinations between certain bases are fixed (C-G and A-T), the sequence of nucleotides in the strand varies.
Since the Coulomb force drops with distance the distances between the base pairs must be small enough that the electrostatic force is sufficient to hold them together.
DNA is a highly charged molecule, with about 2qe (fundamental charge) per 0.3 × 10^−9 m. The distance separating the two strands that make up the DNA structure is about 1 nm, while the distance separating the individual atoms within each base is about 0.3 nm.
Applications of Electrostatics - Aside 2
Smoke Precipitators and Electrostatic Air Cleaning (And Air Ionizers)
Another important application of electrostatics is found in air cleaners, both large and small. The electrostatic part of the process places excess (usually positive) charge on smoke, dust, pollen, and other particles in the air and then passes the air through an oppositely charged grid that attracts and retains the charged particles. (See Figure 5.)
Large electrostatic precipitators are used industrially to remove over 99% of the particles from stack gas emissions associated with the burning of coal and oil. Home precipitators, often in conjunction with the home heating and air conditioning system, are very effective in removing polluting particles, irritants, and allergens.
(a) Schematic of an electrostatic precipitator. Air is passed through grids of opposite charge. The first grid charges airborne particles, while the second attracts and collects them. (b) The dramatic effect of electrostatic precipitators is seen by the absence of smoke from this power plant. (credit: Cmdalgleish, Wikimedia Commons)
Smoke Precipitators and Electrostatic Air Cleaning (And Air Ionizers)
Another important application of electrostatics is found in air cleaners, both large and small. The electrostatic part of the process places excess (usually positive) charge on smoke, dust, pollen, and other particles in the air and then passes the air through an oppositely charged grid that attracts and retains the charged particles. (See Figure 5.)
Large electrostatic precipitators are used industrially to remove over 99% of the particles from stack gas emissions associated with the burning of coal and oil. Home precipitators, often in conjunction with the home heating and air conditioning system, are very effective in removing polluting particles, irritants, and allergens.
(a) Schematic of an electrostatic precipitator. Air is passed through grids of opposite charge. The first grid charges airborne particles, while the second attracts and collects them. (b) The dramatic effect of electrostatic precipitators is seen by the absence of smoke from this power plant. (credit: Cmdalgleish, Wikimedia Commons)
Electric Field
Define F = qE
E = F/q
E is called the electric field of the source charge(s). Notice it is a function of position because the separation "r" depends on the location of the field point.
What exactly is an Electric Field?
James Clerk Maxwell identified the field as the space around an electrified object - a space where electric forces act.
Each electric charge produces in its vicinity an electric field that exerts a force on other charges (just like the smell of a skunk repels or perhaps attracts other animals). Field is like sound of one hand clapping. You don't need 2 charges, just one.
Field formulation does away with action at a distance and is very powerful in ALL areas of physics, where forces are mediated by the field (the FIELD produces the force).
The common thread running through most attempts to define the electric field is that fields and forces are closely related. Here's a pragmatic definition: An electric field is the electrical force per unit charge exerted on a charged object.
Although philosophers debate the true meaning of the electric field, practical problems can be solved thinking of the electric field at any location as the Number of newtons of electrical force exerted on each coulomb of charge at that location.
E = F/q
The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, and by time-varying magnetic fields.
So really all we are doing is taking Coulombs law and dividing by q. What this gives us is the FIELD around ONE (or more by superposition) source charges. That way it defines all of space no matter where we place the other "test charge".
It is helpful to visualize the electric field in the vicinity of a charged object.
Try to get used to this field formulation because we'll be using it in electric fields, magnetic fields and even LIGHT! Iron fillings around a bar magnet is probably the easiest example to visualize and it is much like that with electric fields too.
Define F = qE
E = F/q
E is called the electric field of the source charge(s). Notice it is a function of position because the separation "r" depends on the location of the field point.
What exactly is an Electric Field?
James Clerk Maxwell identified the field as the space around an electrified object - a space where electric forces act.
Each electric charge produces in its vicinity an electric field that exerts a force on other charges (just like the smell of a skunk repels or perhaps attracts other animals). Field is like sound of one hand clapping. You don't need 2 charges, just one.
Field formulation does away with action at a distance and is very powerful in ALL areas of physics, where forces are mediated by the field (the FIELD produces the force).
The common thread running through most attempts to define the electric field is that fields and forces are closely related. Here's a pragmatic definition: An electric field is the electrical force per unit charge exerted on a charged object.
Although philosophers debate the true meaning of the electric field, practical problems can be solved thinking of the electric field at any location as the Number of newtons of electrical force exerted on each coulomb of charge at that location.
E = F/q
The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, and by time-varying magnetic fields.
So really all we are doing is taking Coulombs law and dividing by q. What this gives us is the FIELD around ONE (or more by superposition) source charges. That way it defines all of space no matter where we place the other "test charge".
It is helpful to visualize the electric field in the vicinity of a charged object.
Try to get used to this field formulation because we'll be using it in electric fields, magnetic fields and even LIGHT! Iron fillings around a bar magnet is probably the easiest example to visualize and it is much like that with electric fields too.
Electric Fields and Lightning - Video Demonstration
Visualizing Force Fields Around Charges - Electric Field
You can draw the Electric field vector at each point and join the vectors. When you join the lines you lose information on magnitude of field.
Due to the miraculous property of the coulomb force, namely that it falls like 1 over r^2, there is information even on the strength of the electric field, and that information is contained in the density of electric field lines.
By density of lines, I mean the number of lines crossing a surface perpendicular to the lines, divided by the area of that surface.
To understand Electric Field Flux (which we are going to talk about next), try to see this field lines as a FLOW of the electric field out from a positive charge (like a faucet flowing water out), and a Flow of electric field INTO a negative charge, like a drain. Fluid flow and flux is mathematically isomorphic (same form) to electric field flow/flux.
**Gravitational Force is similar except because of inertia of mass gravitational FIELD is proportional to gravitational force (no need to divide by mass like you have to divide by charge). The deep reason for this is that gravity is the curvature of spacetime and the gravitational field is a geometrical.
You can draw the Electric field vector at each point and join the vectors. When you join the lines you lose information on magnitude of field.
Due to the miraculous property of the coulomb force, namely that it falls like 1 over r^2, there is information even on the strength of the electric field, and that information is contained in the density of electric field lines.
By density of lines, I mean the number of lines crossing a surface perpendicular to the lines, divided by the area of that surface.
To understand Electric Field Flux (which we are going to talk about next), try to see this field lines as a FLOW of the electric field out from a positive charge (like a faucet flowing water out), and a Flow of electric field INTO a negative charge, like a drain. Fluid flow and flux is mathematically isomorphic (same form) to electric field flow/flux.
**Gravitational Force is similar except because of inertia of mass gravitational FIELD is proportional to gravitational force (no need to divide by mass like you have to divide by charge). The deep reason for this is that gravity is the curvature of spacetime and the gravitational field is a geometrical.
Example of Electric Fields around points, lines, sheets and spheres
Notice even though the Electric Field is a 1/r^2 equation, it is ONLY SO for point charges and spheres of charge (we'll come back to this later magnetic fields as it is part of the BIG LIE with high intensity companies).
Notice even though the Electric Field is a 1/r^2 equation, it is ONLY SO for point charges and spheres of charge (we'll come back to this later magnetic fields as it is part of the BIG LIE with high intensity companies).
Gauss's Law & the Flux of a Vector Field
Gauss's law for electric fields relates the spatial behavior of the electrostatic field to the charge distribution that produces it. It gives the SAME result as Coulombs law, but it is more powerful and many times easier to use mathematically.
Simply put it states: Electric Charge produces an electric field, and the flux of that field passing through any closed surface is proportional to the total charge contained within that surface (divided by the permittivity).
Electric Flux Through a Closed Surface = Qinc/eo
Gauss's law for electric fields relates the spatial behavior of the electrostatic field to the charge distribution that produces it. It gives the SAME result as Coulombs law, but it is more powerful and many times easier to use mathematically.
Simply put it states: Electric Charge produces an electric field, and the flux of that field passing through any closed surface is proportional to the total charge contained within that surface (divided by the permittivity).
Electric Flux Through a Closed Surface = Qinc/eo
The analogy of fluid flow is very helpful in understanding the meaning of "flux" of a vector field such as the electric field. You can think of the flux of a vector field over the surface as the amount of that field that "flows" out through the surface.
So a spherical source would be a like a point source of water spraying at a constant rate out in all directions. If you put a spherical transparent balloon around that point source the total amount of water hitting the surface of the balloon is constant regardless of how big you make the balloon. Try to visualize that.
The flux has to stay constant because the amount of water flow is constant, so a small spherical surface will seem like a large pressure or force but the area is really small. A larger sphere will have less pressure per unit area, but the overall area is much larger.
The point is there is still the same amount of water flowing out. This is because water is ONLY flowing from the point source, otherwise water would have to material out of thin area or vanish to increase or decrease the flux.
LARGE PRESSURE/FORCE*small area = small pressure/force*LARGE AREA
So a spherical source would be a like a point source of water spraying at a constant rate out in all directions. If you put a spherical transparent balloon around that point source the total amount of water hitting the surface of the balloon is constant regardless of how big you make the balloon. Try to visualize that.
The flux has to stay constant because the amount of water flow is constant, so a small spherical surface will seem like a large pressure or force but the area is really small. A larger sphere will have less pressure per unit area, but the overall area is much larger.
The point is there is still the same amount of water flowing out. This is because water is ONLY flowing from the point source, otherwise water would have to material out of thin area or vanish to increase or decrease the flux.
LARGE PRESSURE/FORCE*small area = small pressure/force*LARGE AREA
E (the electric field) in Gauss's law represents the total electric field at each point on the (hopefully) symmetric surface under consideration. In our analogy Electric field is like the water pressure at a given spot on the surface. So in this case an point (or small area) on the smaller sphere has a more pressure or force than a point (or small area) on the larger sphere. Think about it... water pressure will decrease with distance from source, BUT overall water flow is constant. But the electric field is technically the force per unit charge but the idea is similar to fluid flow which is easier to visualize.
Symmetric in our examples will mean spherical/point, cylindrical/line or planar. If the surfaces are not symmetric we need to use Coulombs Law or more advanced mathematical techniques. But the basic principle is easily conveyed with symmetric objects.
Certain Problems that are highly symmetric you can get with Gauss's Law.
Example point charge or sphere: Take the field of a point charge q and compute its surface area on a sphere centered on it. The answer is q/eo independent of the radius of the sphere because the area of the sphere increases by r^2 while the field decreased by 1/r^2 so the flux remains the same. Isn't that amazing!! The 1/r^2 law is mostly geometric based on point charges or source spheres!!
Symmetric in our examples will mean spherical/point, cylindrical/line or planar. If the surfaces are not symmetric we need to use Coulombs Law or more advanced mathematical techniques. But the basic principle is easily conveyed with symmetric objects.
Certain Problems that are highly symmetric you can get with Gauss's Law.
Example point charge or sphere: Take the field of a point charge q and compute its surface area on a sphere centered on it. The answer is q/eo independent of the radius of the sphere because the area of the sphere increases by r^2 while the field decreased by 1/r^2 so the flux remains the same. Isn't that amazing!! The 1/r^2 law is mostly geometric based on point charges or source spheres!!
Notice in these examples ONLY spherical symmetry leads to an inverse square law. This is true with ALL inverse square forces. Lines, planes, rings and other source geometries DO NOT fall off by 1/r^2.
This becomes clear when we DO NOT see a 1/r^2 with charge/current lines, loops, planes and other geometries. That is because we have to integrate over the whole surface the electric field at each point on that surface.
For example, electric field drops off from a long wire of charge by 1/r and the electric field stays the same over a large plane of charge (no dropoff - thing about it, the higher above an infinite plane of charge you go, the MORE charges come into your view... you cannot escape an infinite plane of charge).
Gauss's Law gives the SAME result as Coulombs law for an electric field, BUT it greatly simplifies the equations when there is symmetry, like in spheres, cylinders, sheets of charge, lines of charge, etc. But if this is too confusing, just understand it is giving the same result as Coulombs law of the Electric Field around a charge source ANY distance away.
Some Cases Like a Circular Loop of Charge are Symmetric But It is Easier to Just Calculate the Electric Field By Brute Force. The reason this is important is that PEMF devices use circular current loops. This will become obvious later on. This helps us to EXPOSE the BIG LIE many High Intensity PEMF companies and so called experts say that PEMF fields drop off by 1/r^2... That is simply BAD BAD Science!!
This becomes clear when we DO NOT see a 1/r^2 with charge/current lines, loops, planes and other geometries. That is because we have to integrate over the whole surface the electric field at each point on that surface.
For example, electric field drops off from a long wire of charge by 1/r and the electric field stays the same over a large plane of charge (no dropoff - thing about it, the higher above an infinite plane of charge you go, the MORE charges come into your view... you cannot escape an infinite plane of charge).
Gauss's Law gives the SAME result as Coulombs law for an electric field, BUT it greatly simplifies the equations when there is symmetry, like in spheres, cylinders, sheets of charge, lines of charge, etc. But if this is too confusing, just understand it is giving the same result as Coulombs law of the Electric Field around a charge source ANY distance away.
Some Cases Like a Circular Loop of Charge are Symmetric But It is Easier to Just Calculate the Electric Field By Brute Force. The reason this is important is that PEMF devices use circular current loops. This will become obvious later on. This helps us to EXPOSE the BIG LIE many High Intensity PEMF companies and so called experts say that PEMF fields drop off by 1/r^2... That is simply BAD BAD Science!!