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Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.
Maxwell's Equations are a set of 4 complicated equations that describe the world of electromagnetics. These equations describe how electric and magnetic fields propagate, interact, and how they are influenced by objects.
Maxwell’s equations, four equations that, together, form a complete description of the production and interrelation of electric and magnetic fields. The physicist James Clerk Maxwell, in the 19th century, based his description of electromagnetic fields on these four equations, which express experimental laws.
Maxwell’s equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be immediately apparent. Faraday’s law describes how changing magnetic fields produce electric fields.
Maxwell’s equations in understanding the creation of electric and magnetic fields from electric charges and current. Also, the four Maxwell equations are Gauss law, Gauss magnetism law, Faraday’s law, and Ampere law.
Maxwell’s equations have led us to a new kind of equation for the potentials $\phi$ and $\FLPA$ but to the same mathematical form for all four functions $\phi$, $A_x$, $A_y$, and $A_z$. Once we learn how to solve these equations, we can get $\FLPB$ and $\FLPE$ from $\FLPcurl{\FLPA}$ and $-\FLPgrad{\phi}-\ddpl{\FLPA}{t}$.
Maxwell's equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field.