What Is A Field?
Merriam-Webster defines a field as a "region or space in which a given effect
For example, a
charged particle distorts its surrounding space in such a way that
another charged particle 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 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):
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
force of 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.
Charles-Augustin de Coulomb determined that the magnitude of the
electric force (FE) between
two charges (q1 & q2)
that are separated by a distance r is:
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
constant). Kappa equals 1/4πε0
ε0 (epsilon zero) is the electric permittivity of free space
(its ability to permit an electric field).
Epsilon zero equals
μ0 (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 arise from moving charge whether microscopic
(like spinning electrons) or macroscopic (like electron
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
current-carrying 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.
Moving charge not only creates
a magnetic field, it also reacts to one, including its
Electricity and magnetism are coupled aspects of a single, electromagnetic
The electromagnetic force tugs on a moving charge perpendicular to both
its velocity (v) and the surrounding magnetic field (B).
The force (F) on a positive electric charge moving through a magnetic field
is illustrated below.
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.
Magnetic Flux Density (B)
Flux (symbol Phi Φ)
is the flow of field lines through a unit of area perpendicular to the
Flux density is the net amount of flux leaving or
entering a closed surface.
The magnetic flux density (B)
at any point in a magnetic field
is simply defined as the magnetic force F
that would be
felt there by a charge q moving at velocity v
per unit of charge and velocity, of course.
B = F/qv
F = qvB
But there's one more variable ‒ the angle between the charge's velocity
and the direction of the magnetic field. The force is greatest on a charge moving
perpendicular to the
magnetic flux and zero on a charge moving parallel to it.
A vector cross product is therefore needed in our
The unit of magnetic flux density (B)
is the tesla, abbreviated T (capital T because Tesla was a person). A
is the gauss, abbreviated G because Gauss was a person. There are 10,000 gauss in a tesla.
1 T = 10 kG
From B=F/qv, we see that we could also
call a tesla a newton per ampere-meter.
Magnetic Field Strength (H)
In materials like iron, electron spins and their magnetic fields will
with any external magnetic field, adding to the total flux density.
Such materials are said to be magnetically permeable.
Magnetic field strength (symbol H)
does not include the effect of a region's permeability. To
calculate flux density (B) from field strength (H) in free space, the permeability of free
space (μ0) must be factored in:
B = μ0H
The factor μ0 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).
One A/m is the magnetic strength of a coiled wire passing one ampere of
current per meter of coil length (not wire length).
It relates to flux density as follows:
1 A/m = 1.2567 microteslas = 0.012567 gauss
If a region's permeability isn't μ0,
another factor is needed to calculate B
from H. This "dimensionless" constant is
called the relative permeability (μr) of the material:
B = μrμ0H
Relative permeability is determined by experiment.
Lorentz Force Law
The Lorentz force law simply adds the magnetic force to the electric force.
electric aspect comes from equation 1:
The magnetic aspect comes from equation 3:
The sum of these forces describes the total electromagnetic force on a charged
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
In physics, electromagnetism was the first field theory. The electromagnetic
force is transmitted by virtual photons—quantum
fluctuations in the electromagnetic field.