Maxwell’s set of four equations forming the basis for electromagnetism are as important as Newton’s laws in mechanics. Maxwell’s equations are applied in almost all modern technologies. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. Firstly let us see these four sweet equations one by one and then discuss them as a whole.
1. Gauss’ Law or Maxwell’s first equation
Electric charges produce an electric field. The electric flux across a closed surface is proportional to the charge enclosed.
2. Gauss’ Law for Magnetism or Maxwell’s second equation
There are no magnetic monopoles. The magnetic flux-and-faradays-law-quantitative across a closed surface is zero.
3. Faraday’s Law or Maxwell’s third equation
Time-varying magnetic fields produce an electric field.
4. Ampere’s Law or Maxwell’s fourth equation
Steady currents and time-varying electric fields (the latter due to Maxwell’s correction) produce a magnetic field.
Maxwell’s Equations as a Whole
As a whole, what do Maxwell’s Equations mean?
Maxwell’s equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in the vacuum, the “speed of light“. These electromagnetic waves have a wide variety of usage, they are used in small things like routers to big things like search for aliens using radio telescopes and all these devices involves the use of Maxwell’s equations. Maxwell understood the connection between electromagnetic waves and light with these equations in 1861, thereby unifying the theories of electromagnetism and optics.
Using these equations only we got a relation between the speed of light (an electromagnetic wave) and permeability and permittivity of free space. So now you know why the speed of light depends on the medium it is traveling in.
So, I hope you got the essence of Maxwell’s equation. So, if you want to know about these equations in-depth, then consider reading the references.