The beauty of Maxwell’s equations can be seen in how it helps us understand nature as well as instruments, at the same time. Medical devices are simply an advanced understanding that began with understanding electromagnetic waves through Maxwell’s equations.
Each of the following 4 equations has a different name, by which we call’em, but together they are called as the Maxwell’s equations. Together they constitute what I am inspired to say; the golden equations of Physics. If we do some easy tricks they will be converted into whats called as the Wave Equations (of motion) ! Yes, they describe the wave behavior “fully”. — By waves I don’t mean sound waves, but any sort of waves that move at the speed of light. Sound waves are ordinary pressure oscillations, that travel much slower than even rockets.
The 4 equations therefore describe how electromagnetic waves are created and broadcast. Hence TV radio and satellite communication were understood because these 4 equations were understood.
First two are time-independent or static equations.
Gauss law of electrostatics
The first equation is known as Gauss law of electrostatics, it says “Electric fields (E) are a result of sources of electrostatic charges”.
Gauss law of magnetostatics
The second equation is known as Gauss law of static magnetic field ( or magnetostatic field ) it says “apparently there are no sources of magneto-static charge or single magnetic pole from which the magnetic field B is created”.
Then how are magnetic fields created? We needed to know further to find the answer. Lets look at the 3rd and 4th equations.
The last two equations are time-dependent, time varying or dynamic equations. Which is why sometimes we see electro and magneto statics and some times we see electrodynamics and magneto-dynamics or simply electrodynamics, in nomenclature of these fields of studies.
Ampere’s circuital law
The 3rd equation is called as Ampere’s circuital law. Its also whats known as Faraday’s law of electromagnetic induction and Lenz’s law. It says changing magnetic fields can produce electric fields. Not only electrostatic charge but changing magnetic fields as well produce electric fields. Although we don’t know yet how the magnetic fields were produced.
Modified Ampere Circuital law
The last equation is called as Modified Ampere Circuital law or Ampere-Maxwell law.This provides the remaining links in the understanding of Electromagnetic field’s creation and motion. It says magnetic fields are produced by actual electric currents (I) that is; change of electrostatic charges over time produces magnetic fields. Magnetic fields are also produced by changing electrostatic fields, this type of pseudo current is called as Displacement current.