Maxwell’s Equations, a set of four equations that articulate the relationship between electric charge, magnetic field, electric field, and electric current, were first presented by Heaviside and Gibbs in 1884. Only one of the equations was developed by Maxwell himself. Another set of eight equations, derived from Maxwell’s 1865 work, contains six equations built into a scheme of three sub-equations. Both sets continue to inform the study of electromagnetism.
Maxwell’s equations deal with four distinct equations that deal with the subject of electromagnetism. Interestingly, the originator of these equations was not the person who chose to extract these four equations from a larger body of work and present them as a distinct and authoritative group. First presented by Oliver Heaviside and William Gibbs in 1884, the formal structure of Maxwell’s Equations is based on the work of James Clerk Maxwell during the 1860s.
Each of the four components of the set of equations is configured to address four different aspects of electromagnetism. As a group, Maxwell’s Equations seek to articulate the relationship that exists between electric charge, magnetic field, electric field, and electric current. Of the four equations that are part of this group, only one was actually developed by Maxwell himself. The other three were pre-existing understandings postulated by others in the field and interpreted by Maxwell in his 1861 work On Physical Lines of Force.
However, the explanations provided by Maxwell, along with the way he linked the foundations of Ampere’s law, Faraday’s law and Gauss’s law, proved to be a compelling quest and were widely received. With only a few minor modifications to allow for advances in the study of electromagnetism, Gibbs and Heaviside extracted these four elements from Maxwell’s earlier work and called the combination Maxwell’s Equations.
There is also a second set of Maxwell’s equations which is sometimes confused with the first set of four. Derived from Maxwell’s 1865 work “A Dynamical Theory of the Electromagnetic Field”, this combination of equations totals eight. Within this body of eight equations, six of them are actually built into a scheme that contains a set of three sub-equations. In terms of the relationship between the ideas underlying the equations contained in each distinct set, the set of four equations is roughly equivalent to the ideas found in the larger set of eight more complicated equations.
Whether it is Maxwell’s set of four equations or the larger and more complete set of eight, the concepts contained in the equations continue to inform the study of electromagnetism.
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