What Is A Field?

ELECTRIC FIELDS

MerriamWebster defines a field as "a region or space in which a given effect
exists".
For example, a
charged particle distorts its surrounding space in such a way that
another charge is either repelled or attracted, depending on whether
the charges have the same or the opposite polarity.
This electric force is directed along the straight line between the two
charges. Since it has
both a value and a direction, force is a vector. The
mathematical symbol for a force vector is:
The standard unit of force is the newton, abbreviated N (capital N because Newton was a person).
The "region or space" wherein the electric force exists is the
electric field.

Electric Field Strength (E)

The electric field strength (symbol E)
at any point in an electric field is simply defined as the force (F) that a
unit of positive charge would feel
there, per unit of the field's source charge (q):


[1]

Like force,
E is a vector. And since the unit of
charge is the coulomb (C), the unit of
electric field strength (E) is the newton per coulomb (N/C).
An equivalent unit of field strength is the volt per meter—the
strength created by a one volt
potential between two parallel conductive plates one meter apart. One V/m is exactly one N/C.
1 V/m = 1 N/C
By convention, electric fields point in the direction that a positive
test charge would move—that is, away from positive
and toward negative charge:
The field lines in the above illustration are a crude but helpful way
to picture a force field. The electric field strength is greater where the lines
are closer together. The direction of the field at any
particular point is tangent
to the field line.

Coulomb's Law

CharlesAugustin de Coulomb determined that the magnitude of the
electric force (F_{E}) between
two charges (q_{1} & q_{2})
that are separated by a distance r is:


[2]

This equation looks like Newton's law of gravitational force—just
replace the two charges with two masses and put a different constant up front.
The electric constant is κ (kappa
or Coulomb's
constant). It equals 1/4πε_{0}
where
ε_{0} (epsilon zero) is the electric permittivity of free space
(its ability to permit an electric field).
The constant ε_{0} equals
1/μ_{0}c^{2} where
μ_{0} (mu zero) is the magnetic permeability
of free space (its ability to hold a magnetic field) and
c is the speed of light.

MAGNETIC FIELDS

Magnetic fields arise from moving charge whether microscopic
(like spinning or orbiting electrons) or macroscopic (like electron
current
through a wire).
The magnetic field lines surrounding a bar magnet are depicted here.
The field is due to aligned
electron spins in the bar.
One end of the bar is called the north pole and the other, the south.
Poles always come in pairs and, by convention, the field lines point
from north to south.
Note the magnetic compass needles in the drawing ‒ opposite poles
attract and like poles repel. The Earth's geographic north pole is a magnetic south pole.
The magnetic field around a
currentcarrying wire is illustrated below. The yellow disc is
the cross section of a wire whose current
flows into the page ("x" represents the tail of an arrow).
The magnetic field lines curl around the current.
If you point your right thumb in the direction of the
current, your fingers will curl in the direction of the field.
An opposite current would produce an opposite rotation.
Unlike electric field lines, magnetic field lines have no beginning or
end—they're all closed loops. That's because the magnetic north and
south poles are a united dipole, unlike the separated plus and
minus electric charges, called monopoles.

Magnetic
Flux Density (B)

Magnetic flux density (symbol B)
quantifies the density
of the magnetic field lines or flux (symbol Φ Phi)
crossing a unit of area perpendicular to the flux.
At any point in a magnetic field, B is simply defined
to be the force
(F)
that an imaginary northmonopole would feel at that point per unit of the
magnetic field's source charge (q)
and velocity (v). Symbolically,
B = F/qv
However, since the magnitude and direction of the force both depend on the angle between
v and B,
the above equation must be written as a vector cross product:


[3]

The unit of magnetic flux density is the tesla, abbreviated T (capital T
because Tesla was a person). A smaller unit
is the gauss (abbreviated G because Gauss was a person). There are 10,000 gauss in a tesla.

Magnetic Field Strength (H)

In materials like iron, electron spins (and so their magnetic fields) align
with the polarity of any surrounding magnetic field, adding to its overall strength.
Such materials are magnetically permeable.
We've already seen that the magnetic permeability of free space
(μ_{0}) determines
Coulomb's constant
and the force between two electric charges.
Magnetic field strength (symbol H)
doesn't take into account a region's permeability.
In free space, μ_{0} is
needed to convert field strength to flux density:
B = μ_{0}H
The factor μ_{0} is
a "dimensional" constant—that is, it has units.
So while the unit of flux density
(B) is the tesla, the unit of field strength
(H) is the ampere per meter (A/m).
1 A/m = 1.2567 microteslas = 0.012567 gauss
One A/m is the magnetic strength of a coiled wire passing one ampere of
current per meter of coil length, not wire length.
When a region's permeability isn't μ_{0},
another factor is needed to convert H
to B. This dimensionless constant is
called the relative permeability (μ_{r}) of the material:
B = μ_{r}μ_{0}H
Relative permeability is determined by experiment.

ELECTROMAGNETISM

Electricity and magnetism are two tightly intertwined aspects of a
single, electromagnetic force. For example,
moving charge not only creates
a magnetic field but also reacts to a magnetic field—including its own!
The force on a positive charge moving through a magnetic field is
shown below.
The force is perpendicular to both the charge velocity (v)
and the external magnetic field (B).
If you open your right hand and point its thumb in the direction of the charge's
velocity and point its fingers in the direction of the magnetic
field, then your palm will point in the direction of the electromagnetic force.

Lorentz Force Law

The Lorentz force law simply adds the magnetic force to the electric force.
The
electric aspect comes from equation 1:


[1b] 
The magnetic aspect comes from equation 3:


[3] 
The sum of these forces describes the total electromagnetic force on a charged
particle:


[4]


Field Theory

The previous equation, formulated by Hendrik Antoon Lorentz in
1895, embodies modern classical electromagnetism. In essence,
equation 4 is the definition of E
and B. They're the fields
needed to account for the force F.
The Lorentz force law is the culmination of the shift from the idea of
action at a distance ‒ forces reaching out across empty
space without a mechanism or speed limit ‒ to the idea of a field.
A "field" is the medium or mechanism that transmits stress
across a distance, from quantum to neighboring quantum at a finite
speed.
In physics, electromagnetism was the first field theory. The electromagnetic
force is transmitted by virtual photons—quantum
fluctuations in the electromagnetic field.



