What are Maxwell's Equations?

Maxwell's equations are a set of partial differential equations describing the relationship between electric and magnetic fields, charge density, and current density, established by the British physicist James Clark Maxwell in the 19th century. Maxwell's equations consist of Gauss's law that describes how electric charges generate an electric field, Gaussian magnetic law that discusses the absence of magnetic monopoles, Maxwell's law that describes how a current and a time-varying electric field generate a magnetic field, and Faraday's law that describes how a time-varying magnetic field generates an electric field Wait for four equations. It reflects the law that the electric field E and magnetic field B evolve over time under the premise of the field source (charge density and current density J), that is, describes how the field source affects the evolution of the electromagnetic field. However, the electromagnetic field in turn exerts an effect on the field source (charged particles) according to the Lorentz force formula. ^[1]

In Maxwell's equations, E and B are the basic physical quantities of the electromagnetic field, they represent the total macro electromagnetic field in the medium, and D and H are just the two auxiliary field quantities introduced. The relationship between E and D, B and H and the electromagnetic field in matter Related to the nature. For isotropic linear matter, they have the following simple relationship:

In the formula, and are two scalar quantities, which are called dielectric constant (or conductivity) and magnetic permeability, respectively. In a vacuum,

For non-magnetic substances,

Maxwell used these four equations to calculate the speed of electromagnetic waves and found that the speed of electromagnetic waves is the same as the speed of light. So he predicted that the essence of light was electromagnetic waves, and Hertz proved the correctness of this prediction experimentally.

From Maxwell's equations, it can be concluded that light waves are electromagnetic waves. Maxwell's equations and Lorentz force equations are the basic equations of classical electromagnetics. From the relevant theories of these basic equations, modern power and electronic technologies have been developed. ^[1]

Although some historians believe that Maxwell is not the original creator of modern Maxwell equations, Maxwell did indeed derive all related equations independently while establishing a molecular eddy current model. The four equations of modern Maxwell equations can be found in Maxwell's 1861 paper "On the Lines of Physics", 1865 "The Theory of Dynamics of Electromagnetic Fields" and the second volume of the famous book "General Theory of Electromagnetism" published in 1873 In the fourth episode, Chapter 9, "General Equations of Electromagnetic Fields", you can find recognizable forms, although there are no clues about vector marks or gradient symbols. This textbook, which must be read by physics students in the future, has a release date earlier than the works of Heaviside, Heinrich Hertz, and so on.

James Clerk Maxwell AD 1831-AD 1879

James Clark Maxwell is a great British physicist and founder of classical electromagnetic theory. Born in Edinburgh, Scotland in 1831. His intellectual development was extremely early, when he was only fifteen years old, he submitted a research paper to the Royal College of Edinburgh. He studied at

In extended physics, Maxwell's equations in curved spacetime restrict the dynamics of electromagnetic fields in curved spacetime (the metric in between may not be Minkovsky's). They can be considered as extensions of Maxwell's equations in vacuum in the framework of general relativity, while Maxwell's equations in vacuum are just special forms of generalized Maxwell's equations in locally flat spacetime. However, in the general theory of relativity, the existence of the electromagnetic field can also cause space-time bending, so Maxwell's equations in vacuum should be understood as a convenient approximation. Microscopic Maxwell's equations are only useful for Maxwell's equations in a vacuum. This is also called "microscopic" Maxwell's equations. For Maxwell's equations related to anisotropic matter in the macro, the existence of matter will establish a frame of reference so that the equations are no longer covariant. The geometric description is the same. The electromagnetic field itself requires that its geometric description has nothing to do with coordinate selection, and the geometric description of Maxwell's equations in any space-time is the same regardless of whether the space-time is straight. At the same time, the system of equations in flat Minkowski space will be modified the same when using non-Cartesian local coordinates. For example, the equations in this entry can be written in the form of Maxwell's equations in spherical coordinates. Based on the above reasons, a better understanding method is to understand Maxwell's equations in Minkowski space as a special form, rather than understanding Maxwell's equations in curved space-time as a generalization of relativity.