Fundamental Meaning and Typical Solutions of Maxwell’s Equations

The main objective is to understand the meaning of Maxwell’s equations. It is

a set of four differential equations that describe several fundamental laws that are already

known. Why did these equations cause a revolution in physics? One reason is that the

distribution of the electromagnetic field can be obtained by solving first- or second-order

differential equations. Several examples have been shown to obtain the distribution of

the electric field produced by simple electrodes. The three-dimensional trapping of

charged matter can be achieved via two methods: the combination of a DC electric field

and a DC magnetic field or using an AC electric field.

The most important aspect of Maxwell’s equation is that it elucidates the identity of light

as an electromagnetic wave. Light energy is given as the potential energy of electric and

magnetic fields. Light has momentum and generates radiation pressure on a reflecting

mirror.

The speed of light was determined to be independent of the observer, which was the basis

for the theory of relativity. A fundamental aspect of the theory of special relativity is also

introduced.

Keywords: Ampere’s law, Coulomb’s law, Cyclotron radiation, Electromagnetic wave, Faraday’s law of induction, Gauss’s theorem, Maxwell’s equation, Lorenz transform, Stokes’s theorem, The speed of light, Theory of relativity, Trap of charged matter.

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