# User Contributed Dictionary

### Noun

- The phenomena associated with moving electric charges, and their interaction with electric and magnetic fields; the study of these phenomena

#### Translations

- Swedish: elektrodynamik

# Extensive Definition

Classical electromagnetism (or classical
electrodynamics) is a theory of electromagnetism that
was developed over the course of the 19th
century, most prominently by James
Clerk Maxwell. It provides an excellent description of
electromagnetic phenomena whenever the relevant length scales and field strengths
are large enough that quantum
mechanical effects are negligible (see quantum
electrodynamics).

Maxwell's
equations and the Lorentz force
law form the basis for the theory of classical
electromagnetism.

## Lorentz force

The electromagnetic field exerts the following
force (often called the Lorentz force) on charged
particles:

\mathbf = q\mathbf + q\mathbf \times
\mathbf

where all boldfaced quantities are vectors:
F is the force that a charge q experiences, E is the electric
field at q's location, v is q's velocity, B is the strength of
the magnetic
field at q's position.

## The electric field E

The electric
field E is defined such that, on a stationary charge:

\mathbf = q_0 \mathbf

where q0 is what is known as a test charge. The
size of the charge doesn't really matter, as long as it is small
enough as to not influence the electric field by its mere presence.
What is plain from this definition, though, is that the unit of E
is N/C, or newtons per
coulomb. This unit is
equal to V/m (volts per
meter), see below.

The above definition seems a little bit circular
but, in electrostatics, where charges are not moving, Coulomb's law
works fine. So what we end up with is:

\mathbf = \sum_^ \frac

where n is the number of charges, qi is the
amount of charge associated with the 'i'th charge, ri is the
position of the 'i'th charge, r is the position where the electric
field is being determined, and ε0 is a universal constant called
the
permittivity of free space.

Note: the above is just Coulomb's law, divided by
q1, adding up multiple charges.

Changing the summation to an integral yields the
following:

\mathbf = \int \frac \mathrmV

where ρ is the charge
density as a function of position, runit is the unit vector
pointing from dV to the point in space E is being calculated at,
and r is the distance from the point E is being calculated at to
the point charge.

Both of the above equations are cumbersome,
especially if one wants to calculate E as a function of position.
There is, however, a scalar function called the electrical
potential that can help. Electric potential, also called
voltage (the units for which are the volt), which is defined
thus:

\phi_\mathbf = - \int_s \mathbf \cdot
\mathrm\mathbf

where φE is the electric potential, and s is the
path over which the integral is being taken.

Unfortunately, this definition has a caveat. From
Maxwell's equations, it is clear that \nabla \times \mathbf is not
always zero, and hence the scalar potential alone is insufficient
to define the electric field exactly. As a result, one must resort
to adding a correction factor, which is generally done by
subtracting the time derivative of the A vector potential described
below. Whenever the charges are quasistatic, however, this
condition will be essentially met, so there will be few problems.
(As a side note, by using the appropriate gauge transformations,
one can define V to be zero and define E entirely as the negative
time derivative of A, however, this is rarely done because a) it's
a hassle and more important, b) it no longer satisfies the
requirements of the Lorenz gauge and hence is no longer
relativistically invariant).

From the definition of charge, it is trivial to
show that the electric potential of a point charge as a function of
position is:

\phi = \frac

where q is the point charge's charge, r is the
position, and rq is the position of the point charge. The potential
for a general distribution of charge ends up being:

\phi = \frac \int \frac\, \mathrmV

where ρ is the charge density as a function of
position, and r is the distance from the volume element
\mathrmV.

Note well that φ is a scalar, which means that it
will add to other potential fields as a scalar. This makes it
relatively easy to break complex problems down in to simple parts
and add their potentials. Taking the definition of φ backwards, we
see that the electric field is just the negative gradient (the
del operator) of the
potential. Or:

\mathbf = -\nabla \phi

From this formula it is clear that E can be
expressed in V/m (volts per meter).

## Electromagnetic waves

A changing electromagnetic field propagates away
from its origin in the form of a wave. These waves travel in vacuum
at the speed of
light and exist in a wide spectrum
of wavelengths.
Examples of the dynamic fields of electromagnetic
radiation (in order of increasing frequency): radio waves, microwaves, light (infrared, visible
light and ultraviolet), x-rays and gamma rays. In
the field of particle
physics this electromagnetic radiation is the manifestation of
the electromagnetic
interaction between charged particles.

## General field equations

As simple and satisfying as Coulomb's equation may be, it is not entirely correct in the context of classical electromagnetism. Problems arise because changes in charge distributions require a non-zero amount of time to be "felt" elsewhere (required by special relativity). Disturbances of the electric field due to a charge propagate at the speed of light.For the fields of general charge distributions,
the retarded potentials can be computed and differentiated
accordingly to yield Jefimenko's
Equations.

Retarded potentials can also be derived for point
charges, and the equations are known as the
Liénard-Wiechert potentials. The scalar
potential is:

\phi = \frac \frac

where q is the point charge's charge and \mathbf
is the position. \mathbf_q and \mathbf are the position and
velocity of the charge, respectively, as a function of retarded
time. The vector
potential is similar:

\mathbf = \frac \frac

These can then be differentiated accordingly to
obtain the complete field equations for a moving point
particle.

## See also

electrodynamics in Catalan: Electrodinàmica
clàssica

electrodynamics in Danish: Elektrodynamik

electrodynamics in Galician: Electrodinámica
clásica

electrodynamics in Korean: 전자기역학

electrodynamics in Hebrew: תורת החשמל והמגנטיות
הקלאסית

electrodynamics in Hungarian:
Elektrodinamika

electrodynamics in Dutch: Elektrodynamica

electrodynamics in Swedish: Klassisk
elektrodynamik