30.12: Maxwell’s Equation Of Electromagnetism

James Clerk Maxwell (1831–1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major contributions to the development of the kinetic theory of gases, to the understanding of color vision, and to understanding the nature of Saturn's rings. He is probably best known for having combined existing knowledge on the laws of electricity and magnetism with his insights into a complete overarching electromagnetic theory, which is represented by Maxwell's equations.

The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday. Maxwell discovered logical inconsistencies in these earlier results and identified the incompleteness of Ampère's law as their cause.

Maxwell's equations led to the prediction of electromagnetic waves that can travel through space without a material medium, implying that the speed of electromagnetic waves is equal to the speed of light. Prior to Maxwell's work, experiments had already indicated that light was a wave phenomenon, although the nature of the waves was yet unknown. So, light was known to be a wave, and Maxwell predicted the existence of electromagnetic waves that traveled at the speed of light.

The conclusion seemed inescapable that light must be a form of electromagnetic radiation. However, Maxwell's theory showed that other wavelengths and frequencies than those of light were possible for electromagnetic waves. He showed that electromagnetic radiation with the same fundamental properties as visible light should exist at any frequency. It remained for others to test and confirm this prediction.

All basic interactions of electromagnetism can be explained in terms of four fundamental equations called Maxwell's equations, which were combined by Maxwell.

The first equation is Gauss's law of electrostatics, which states that the net electric flux through any closed surface equals the net charge enclosed by the surface divided by the permittivity of the free space.

This signifies that the total flux through a closed surface depends only on the charge enclosed by it.

The second equation is Gauss's law of magnetism, which states that the magnetic flux through any closed surface is always zero. This implies that magnetic monopoles do not exist.

The third equation is Faraday's law. This states that a changing magnetic flux produces an induced emf and an induced electric field.

The induced emf in a closed loop equals the negative of the time derivative of the magnetic flux through that loop.

The fourth equation is a modified form of Ampere's law and is called the Ampere-Maxwell law. For this, Maxwell added a term for the displacement current to the existing Ampere's law equation.