The lodestone was probably man's first experience with the behavior of charged particles.  Lodestone, the mineral magnetite, can be put in a little boat, floated on water, and it tells the cognoscenti what direction is North.  Magic!

The lodestone eventually got replaced with needles of iron suitably "magnetized" and suspended on delicate swivels.  The magentic compass served seamen the world round.

Electricity got discovered, and even in the middle of the 20th century school teachers told us that "nobody really knows what electricity really is."  That was one of the fine, old and crusty misconceptions that saturated the market of ideas then:  The school teachers and their students indeed had little understanding of electricity, but the scientists knew a very great deal about it.  Electricity is the behavior of charged particles (electrons and protons), which are ubiquitous components of all material things, including ourselves.  Electric currents are the motions of charged particles, usually, but not always, in metal wires.

Several phenomena were recognized then and given names which were metaphorical relationships to other observations of nature. "Voltage" was like water pressure in pipes.  "Amperage" was like quantity of water flowing in pipes.  "Resistance" (in "ohms") was like the resistance that pipes give to the flow of water.  A mathematical relationship between voltage, amperage, and resistance was seen to be a pretty good approximation for predicting electrical current: amperage is proportional to voltage, and the "constant of proportionality" is related to electrical resistance.  This "Ohm's law" is only an approximation, however, and it only hints at what is happening inside the wires.

A couple of centuries ago, someone discovered that a coil of wire carrying an electric current behaved just like a lodestone.  It is an "electromagnet."  It can be made into a compass, into an electric motor, an electric meter, a solenoid to put into an automobile starting device...  The technology of electromagnets was quickly developed into many industries.

All this time, a few people were systematically observing and experimenting with all of these "electromagnetic" behaviors.  The "electric field" and the "magnetic field" were born from these experiments.  The fields are inventions of human minds working in the metaphor and mathematics realms of human thinking.  They represent man's observations of charged particles.

But, at first, men still did not know that matter is composed of very, very tiny "particles" which were to get named "electrons," "protons," "neutrons," "photons," "neutrinos," "positrons," etc.  That came later and would demonstrate that there are realms beyond human perception, imagination, metaphor, and mathematics.  It's a world that appears to man as magic.

Rub a pitch ball with cat fur and you get a "static charge" which makes all kinds of things behave peculiarly.  These "electrostatic" forces were studied in great detail and certain mathematical laws became recognized.  Rub more and you get more effect:  This new property of matter could be measured and quantities assigned.  Double the quantity and you double the effect.  The closer two objects carrying a charge are to each other,  the greater the effect: Twice as close gives four times the effect.  The effect goes as the distance squared.  And there are two "kinds" of charge: when the two kinds are different, they attract each other, and when they are the same, they repel.

Here it was that imagination, conjoined with the recognition of these patterns, gave birth to the electrostatic "field."  The field is just a convenient fiction that lets us visualize how these invisible particles behave.

We start by imagining a "unit" of charge somehow (magically, perhaps) parked in a  spot so that it can't move. The unit is the "coulomb" (6.24145994 X 10¹⁹ electrons, more or less).  The spot we place it will be the origin of our reference frame (X = 0, Y = 0, Z = 0).  Finally we take a "test charge," also one coulomb in size and make a map of the force on the test charge everywhere in space, assiging a separate force for each and every point in the space.

We let the "test" charge be one coulomb simply for later convenience.  We could have used any size of "test" charge and divided the force by the magnitude of the test charge. That would give us a map of force-divided-by-charge.  All we need do then is look up the value of force-divided-by-charge for any given point in space, multiply that value by the quantity of charge for any object, and that gives us the electrostatic force on that object at that point.  That force-divided-by-charge is the electric field:

The map of force-divided-by-charge (a value for every point in space) is the electrostatic field.  Because that's its definition.
 

Anything whatsoever which has a measurable value for each and every point in space is a FIELD.  The temperature of the air is a field.  The velocity of the air is a field.  The velocity of water flow in a stream is a field.

A field is not necessarily a "force field."  The electrostatic field is certainly not the force: it's the force divided by the size of a test charge.  It's a mathematical abstraction.

Futhermore, the electrostatic field is a vector field.  So is the velocity of air and the velocity of water in a stream.  The temperature of the air is not a vector field: it's a scalar field.
 

The magnetic field is a field of a very different stripe.  Charges in motion behave in most confusing ways.  The magnetic field is an abstraction invented to describe the complications that many people observed over a period of many decades, a result of meticulous experimentation following many outcomes and imaginative hypotheses all aimed at making sense to a human mind.

We have to work hard at this one because Mother Nature didn't design the antics of charged particles to be suitable to the skills of a human brain.

The magnetic field is defined so that it, too, is a vector field (having a direction and a magnitude—that is, three components—at each point in space).  Then, the "magnetic force" on a "test" charge has these weird characteristics:  As with the electrostatic force, it's magnitude will be proportional to the size of the test charge, but it's also proportional to the size of its velocity but in a very peculiar way.   If the velocity and the field are perpendicular, the magnetic force is a maximum.  If the velocity and the field are parallel, the "magnetic force" is zero.  The magnetic force is always perpendicular to both the velocity and the magnetic field.

I'm sure Mother Nature is very sorry that these affairs are so confusing to the human mind, but the behaviors of electrons and protons are not something designed to be understandable to human minds.  Those behaviors are, however, what underlies the workings of the human mind—and everything else in the universe that contains charged particles.

The two fields, electrostatic and magnetic, are what a human being needs to see to have a sense of over a century of meticulous observations of things causd by that very peculiar property, charge.

There is a catch.  (Actually, there are several catches.)  The fields are not the "reality."  The behavior of the charged particles is the reality.  They are not really separate entities, they are separate only in our minds—because the reality is simply beyond our meager thinking abilities, our abilities to see the patterns of the behaviors.

And so we say that a magnetic field is "created" by the motion of charged particles.  The electrostatic field is always there simply because the particles have charge.  We say that the force on a charge is the sum of the magnetic and electrrostatic "components" from the "two fields."

That was the state of affairs in human knowledge of "electromagnetic fields" in the first year of the 20th century.  Pretty good, but a few good mathematicians saw some serious problems.  The solutions to those problems would come out of the "magic" realm that lies beyond human comprehension.  There were problems with our electromagnetic theory when we look from frames of reference that are moving with respect to what we are measuring.

What if we happen to be moving with the "moving" charge that "created the magnetic field"?  Relative to our viewpoint, it isn't moving any more, so it doesn't create a magnetic field.  It creates only an electrostatic field.  We have destroyed the magnetic field simply by arbitrarily choosing to view things from a different viewpoint.  Mind over matter!

If there is a fixed point in the universe we could refer everything to that point and there is no problem.  The existence of a magnetic field doesn't depend on our arbitrary choice of  whether we "move with the charge" or "don't move with the charge" when we look at it.  The laws of phyiscs are independent of our arbitrary choices.

Some MAGIC would enter the MATHEMATICS realms of abstract reality during the first decade of the 20th century.  Rewriting the physical laws, the equations of physics, so as to make the laws describe all those centuries of observations and still be independent of arbitrary human choices was the genius of Einstein's Theory of Special Relativity.

The magnetic field and the electrostatic field are two inseverable parts of a mathematical and metaphorical description of our world.  Our theory of the charge part of the world has always had one foot in the realm of magic, the reality that mystifies.  When Einstein resolved the dissonances of relative motions, he revealed new mysteries.  Mass and energy are related by logical equivalence.  The speed of light in a vacuum is a constant of nature.  Simultaneity is an ambiguous concept.
 

Two decades after Einstein published his solution to the puzzles of moving charged particles, new dissonances were discovered that revealed that the measured values of physical parameters could not have just any value whatsoever: their values "jump" from one step to the next without passing through intermediate values.  They are "quantized."

Quantum mechanics revealed that our metaphors drawn from our perceptions break down when we look at electrons, atoms, and molecules.  The "orbits" of electrons about the atom's nucleus are very unlike the orbits of planets about the sun.

Quantum mechanics revealed that many things which our metaphors make us think are separate and independent are actually inseverable parts of wholes in that realm of  magic beyond any easy human comprehension—just like the electric and magnetic fields.  Energy and time conjoin to form an inseverable whole in the uncertainty principle.  So do position and momentum (and angular position and angular momentum).

Many wishful thinkers, looking for evidence that our minds might control matter simply by thinking, look to the uncertainty principle to confirm their wish.  They then separate the inseverable in their minds and get results that have little chance of representing the realities of quantum mechanics...or of the world.  Quantum mechanics is a millipede with most of its feet in the realm of abstract magic beyond human comprehension. 
 

The world would be much more human-friendly if we could control its behavior with our thoughts about it, if reality responded to our arbitrary thoughts and wishes.  If we could predict the future by willing the future.

The word "magnet" comes from Magnesia, a region of ancient Thessaly, where lodestone was rather common.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

A person might point to the fact that some person in ____fill in the blank___ actually won the big lottery.  "If that person  won the lottery, then so could I!"  That statement, if offered as evidence that the statistical reasons for not playing the lottery are invalid, appeals to the residue of observations which slips through the statistical sieve--while ignoring the vast majority of contrary evidence.  It's PAP (the Prove Anything Ploy).

Keith Devlin, in The Math Gene, describes the process of doing mathematics as constructing and furnishing abstract rooms in one's minds that corespond to the abstract relationsips of some mathematical problem.  The solution to the problem then comes, not the result of meticulous following of some learned manipulations, but rather as a sudden "Eureka!" feeling when the answer just falls out of the blue, assembled in its full form as dictated by the structure and patterning of the house.