AnyGrowth8158 t1_ja94eke wrote
They're equations that combined the formerly separate theories of electricity and magnetism. They show how they aren't actually two different forces, but two different aspects of a single phenomenon. It is one of the earlier unifying theories for what would become known as four fundamental forces.

One equation (Gauss's Law) describes the electric field generated by a static charge.

One equation (Gauss's Law for Magnetism) shows that there are no magnetic charges (monopolesalthough some theories postulate their existence no one has found one to date).

One equation (Faraday's Law) shows how an electric field is created by a magnetic field changing in time.

One equation (Ampere's Law) shows how a magnetic field is created by an electric field changing in time.
As you may tell from the equations' names Maxwell did not necessarily come up with the equations, but he put them together and understood many of their implications. Any classical electromagnetic properties can de derived from the equations.
Perhaps the most profound implication of Maxwell's equations are electromagnetic waves. He realized that a changing electric field will generate a changing magnetic field, which in turn would create a changing electric field, which in turn would create a changing magnetic field, ad nauseam. From this he realized that electric and magnetic fields could generate a selfpropagating wave. Combining the equations you can calculate the speed of propagation which just so happens to be the speed of light...
jlcooke t1_ja9jde8 wrote
Central to Maxwell's equations are two values:
 Electric: https://en.wikipedia.org/wiki/Vacuum_permittivity e0 (epsilonnaught), and
 Magnetism: https://en.wikipedia.org/wiki/Vacuum_permeability m0 (munaught)
speed of light = 1 / sqrt(e0 * m0)
PerturbedHamster t1_jaa0p0r wrote
I would say it's really just one number (epsilonnaught). What we call a magnetic field is just the effects of special relativity once you start moving charges. The speed of light is a fundamental property of spacetime, so it shows up once you start making relativistic corrections to electric fields, but you knew that going in so I wouldn't call it a property of electricity & magnetism. Once you have e0 and you know about special relativity, then you know what u0 has to be.
AnyGrowth8158 t1_jaafqzp wrote
In case it's not clear in the above comment a magnetic field arises from the movement of chargeit doesn't matter if you move past the charge or the charge moves past you.
Suppose, we put a charge on a train, and have two sets of electric and magnetic field detectors. Put one set of detectors on the train next to charge, and another on the platform of the station.
When the train is sitting at the station, both detectors will measure an electric field and no magnetic field due to the charge.
Once the train starts moving, the detector on the train will still measure an electric field, but no magnetic field. The detector at the station will measure both an electric and magnetic field.
Repeat the experiment, but this time put the charge on the platform. You get the same result except it is the train detector which will measure both the electric and magnetic field while the detector at the station will measure only an electric field.
Whether or not you measure the magnetic field is dependent upon your reference frame. This was one of the ideas which inspired special relativity.
Chromotron t1_ja9mn0z wrote
(For OP or whoever is interested)
Note how electric and magnetic are (almost) interchangeable, each one induces the other in the same way. The only weirdness is the second rule by which magnetism might not have basic charges ("monopoles") in nature. Otherwise, we would replace (2) by the corresponding variant of (1) to account for free magnetic charges, and the symmetry of the 4 laws would be even more obvious.
Even deeper(?), the 4 equations are actually only one when one interprets magnetic as an imaginary variant of electric. This single equation is
∇F = μ_0 c J.
richtl t1_jaacvp1 wrote
I think Maxwell's equations are one of the most beautiful things in physics. I remember being awestruck by how an entire semester of thermodynamics class simplified to these four simple elegant equations.
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