A: What is the physical meaning of Maxwell's equations?

I am going to use non mathematical imagination to explain this math, so excuse if there are any inconsistencies. This is how our professor back in the school explained it to us.

Think of a stream of water. But let this water be incomprehensible. Hence, there will be no local areas in this stream where water will be more dense or rare. Such a stream will have divergence of zero. And, magnetic field is just like that. You can write it mathematically as –
∇.B = 0
Putting a magnet in magnetic field will be like just putting a PVC pipe open at both ends. Water enters from one end and leaves from another keeping the overall divergence zero.

Now, given that electric charges did not exist in isolation like magnetic poles, we would have ∇.E= 0. However, electric charges do. And putting electric charge in a stream is more like inserting a hose pipe in the stream that either pushes more water into it with some force or pulls water out of it if attached to vacuum pump. The divergence created depends on how much water is being pushed in or pulled out, which depends on pressure of water and on the size of opening of hose pipe. In the same way electric field lines coming out of a positive charge or falling into the negative charge depends on charge density and permissiveness of free space for the field. Which translates to
∇.E= ρ/ε

Finally, imagine how wind force created waves on surface of ocean and in turn the waves moving creates sound waves in the wind. The music of ocean. Now I don’t think the waves of electric field and magnetic field resembles that. But this is essence of next equation. The equation says the pattern of electric field in space will depend on pattern of how magnetic field is changing in time. I know that this is how light propagates. The magnetic field fluctuations create electric waves and the changing electric field creates magnetic waves in turn.
Which can be written as
∇xE = -∂B/∂t

And something interesting emerges, when we add a moving charge in the stream of electric field lines we know it will create divergence – local fluctuations in this field as it moves. The changing electric field will create magnetic field in turn. This is how a moving charge particles, such as those in wire carrying current creates magnetic field around it.
You may write this as
Magnetic field created in space perpendicular to electric field depends on the density of moving charge given permeability f it in space + the how electric field is changing in time given the permeability and permissivity of space.
Or,

∇xE = uJ + uε∂E/∂t

E is electric field
B is magnetic
u is permeability
ε is permissivity
ρ is charge density
J is density of moving charge or current density.

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