# Electromagnetic Theory

The
study of electromagnetic theory is a very large subject, which this
overview will only attempt to summarise in the context of foundation
science. Today, much of electromagnetic theory is still linked to Maxwell’s
equations, which were first published in 1864, which preceded the re-emergence
of the wave-particle duality debate that arose out of the following
development in the early 20^{th} century:

- Planck’s idea concerning
*quantum energy*in 1900 - Einstein’s 1905 paper on the
*photoelectric effect*that led to the idea of the photon. - Structural development of the
*atomic model*. - Emergence of
*quantum theory*

So, although the wave-particle duality debate had existed since the time of Newton, the publication of Maxwell’s theory took place in a time when light was generally perceived to be a wave. This wave-centric position had slowly strengthen in the 100 years following Newton’s death in 1727 and although the foundations of classical electrodynamics had many contributors, Maxwell’s equations owe much to the work of Coulomb, Ampere, Gauss and Faraday, who laid down many of the basic laws of electromagnetism. These laws helped define and specify the nature of some of the basic terms, which this subject now takes for granted, i.e. charge, force, field, voltage, capacitance, inductance and flux.

- In 1785, Coulomb published an equation relating the force [F]
between two charged particles as being proportional to the magnitude
of the charges [q
_{1}& q_{2}] and inversely proportional to the square of the distance [r] between them, i.e.

[1] F = K(q_{1}*q_{2})/r^{2};
where
K = 1/(4πε).

- The similarities between this equation and Newton’s gravitational equation [2] is highlighted along with the fact that both forces depend on the relationship between two particles, i.e. the force is not an attribute that can be assign to a single particle.

[2] F=G(m_{1}*m_{2})/r^{2}

- However, it should also be highlighted that the gravitational
force is always an `
*attractive`*force, while charge can be both an `*attractive`*and `*repulsive`*force.

- In 1835, Gauss presented an equation that related the
total electric flux out of a closed surface to the charge enclosed
divided by the permittivity, i.e. φ=Q/ε.
- In 1820, Oersted discovered that an electric current could cause
a compass needle to deflect. Equally, a moving electric charge caused
a magnetic field. These observations were interpreted by Ampere
and published in 1826 as Ampere’s law. This law relates the magnetic
field in a closed loop to the electric current passing through the
loop. It is the magnetic equivalent of Faraday's law of induction.
- In 1831, Faraday published his discovery that a changing magnetic field causes an electric voltage. If the magnetic flux through a loop of wire changes, a voltage drop appears at a small break in the wire.

As such, we might begin to recognise the importance of this body
of work to Maxwell’s later insights. In fact, Maxwell’s equation might
be traced backed to the correction he made to Ampère's circuital law
in his 1861 paper entitled ‘*On Physical Lines of Force’*. Subsequently,
in 1864, he published a paper entitled ‘*A Dynamical Theory of the Electromagnetic
Field’ *, although the original form consisted of some 20 equations
that essentially combined and corrected many previous laws:

- A corrected version of Ampere's law.
- Gauss' law for charge.
- The relationship between total and displacement current densities.
- The relationship between magnetic field and the vector potential.
- Faraday’s relationship between electric field and the scalar and vector potentials.
- The relationship between the electric and displacement fields
- Ohm's law relating current density and electric field.
- The continuity equation relating current density and charge density.

Finally, in 1884, Oliver Heaviside reformulated Maxwell's original
system of equations into a differential format based on
*vector calculus*;
although today Heaviside’s differential form have also been complemented
by an integral form. This said, there are essentially only 4 equations
to be discussed, which we might sub-divided into 2 distinct classes
that separate the *time-independent* and* time-dependent*
nature of electromagnetic waves. The term ‘*time- independent‘ *
essentially defines the scope of 'electrostatics', while *
‘time-dependent’* defines the scope of '*electrodynamics'*

The diagram above tries to initially illustrate the concept of a
self-propagating, self-perpetuating EM wave moving through the vacuum
of space, i.e. with no direct reference to any supporting media. As
such, we might initially visualise an EM wave as some sort of transverse
wave, analogous to the motion of simple harmonic oscillation, in which
energy is somehow conserved in propagation.