The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible.
The physical phenomena that electromagnetism describes have been studied as separate fields since antiquity.
For example, there were many advances in the field of optics centuries before light was understood to be an electromagnetic wave.
However, the theory of electromagnetism, as it is currently understood, grew out of Michael Faraday's experiments suggesting the existence of an electromagnetic field and James Clerk Maxwell's use of differential equations to describe it in his A Treatise on Electricity and Magnetism (1873).
Detailed historical accounts are given by Wolfgang Pauli,[1] E. T. Whittaker,[2] Abraham Pais,[3] and Bruce J.
Although the equation appears to suggest that the electric and magnetic fields are independent, the equation can be rewritten in term of four-current (instead of charge) and a single electromagnetic tensor that represents the combined field (
The size of the charge does not really matter, as long as it is small enough not to influence the electric field by its mere presence.
Electric potential, also called voltage (the units for which are the volt), is defined by the line integral where
From Maxwell's equations, it is clear that ∇ × E is not always zero, and hence the scalar potential alone is insufficient to define the electric field exactly.
As a result, one must add a correction factor, which is generally done by subtracting the time derivative of the A vector potential described below.
This makes it relatively easy to break complex problems down into 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.
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.
As simple and satisfying as Coulomb's equation may be, it is not entirely correct in the context of classical electromagnetism.
For the fields of general charge distributions, the retarded potentials can be computed and differentiated accordingly to yield Jefimenko's equations.
The vector potential is similar: These can then be differentiated accordingly to obtain the complete field equations for a moving point particle.
Branches of classical electromagnetism such as optics, electrical and electronic engineering consist of a collection of relevant mathematical models of different degrees of simplification and idealization to enhance the understanding of specific electrodynamics phenomena.
[5] An electrodynamics phenomenon is determined by the particular fields, specific densities of electric charges and currents, and the particular transmission medium.
Since there are infinitely many of them, in modeling there is a need for some typical, representative Fundamental physical aspects of classical electrodynamics are presented in many textbooks.