The Maxwell’s equations, from nature to instruments.
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.
If you are looking for detailed derivations of Maxwell’s equations and other electromagnetic theory lectures ( honors level courses ) see the following linked resources.
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 Maxwell’s equations …
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.
- Faraday’s law
- The 3rd equation is 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’s circuital law
- The last equation is called as Modified Ampere Circuital law or Ampere – Maxwell equation. 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.
So all in all;
- Static electric charges produce electric fields.
- Static electric currents produce magnetic field.
- Changing electric fields produce magnetic fields and
- Changing magnetic fields produce electric fields.
E produces B and B produces E, if they are changing wrt time. In other words if we run towards a magnet, with electric coils on our body, it will produce electric and magnetic fields, on our body, that might kill us by electrocuting, if strong enough. This mechanism of inducing electric and magnetic fields by changing each other, is how we produce electric current and supply to households.
But these 4 equations tell us much more than just how electric currents are produced.
Their advance versions which were developed by Einstein — known as Relativity Theory, and later Schwinger and Feynman — known as Quantum Electrodynamics, and a great many number of other scientists, explains all sorts of phenomena we know today, eg neutrinos that are created in the Sun and move towards earth every second, are studied by employing the laws of electrodynamics.
These advance versions of Maxwell’s equation in terms of QED, explain cosmic charges — which produce aurora-borealis, or northern lights, and fiber optics as well as; electron microscopes, NMR and PET machines found in modern Hospitals.
Aurora Borealis or Northern Lights at Ireland.