[paul cotter]

The solution to the wave equation derived from Maxwell's equation gives three components with factors of 1/r, 1/rsq and 1/rcubed. The near field is the 1/rsq term and the radiated field is the 1/r term.

[hamdani yusuf]

An accelerating charge generates an electromagnetic field.

Except when there's another charge cancelling it, like a pair of electrons moving as a Cooper pair in a superconductor ring, which can retain their kinetic energy for years.

Furthermore, an electric charge moving in constant velocity also generate electromagnetic field.

A stationary electric charge produce electrostatic field.

[alancalverd]

Furthermore, an electric charge moving in constant velocity also generate electromagnetic field.

No. A charge moving at constant speed generates a magnetic field, and the charge itself has an electric field, but there is no radiative EM field. This goes right back to Isaac Newton! 

[evan_au]

Maxwell's Equations...The near field is the 1/rsq term and the radiated field is the 1/r term.

A radiated field of 1/r seems to conflict with what we are taught in high school that the radiated power is 1/r² (the inverse square law).
- I vaguely recall hearing in antenna design that there was a near-field component that fell off like 1/r³ (while the quoted section suggests 1/r²)

How should I interpret Maxwell's Equations in terms of the inverse square law?
- Is the electromagnetic source a point source or a linear source of infinite length (the inverse square law applies to a point source)?
- Does the field intensity correspond to the magnitude of the Electric (or Magnetic field), while the power is proportional to E² (or B²)?
- Can you interpret Maxwell's equations in a semi-quantised way, and say that the probability of finding a photon in a particular location is proportional to the magnitude squared?

https://en.wikipedia.org/wiki/Maxwell%27s_equations#Key_to_the_notation

[alancalverd]

I agree - 1/r² should characterise the far field. 1/r dependence is usually associated with fields within 5d where d is the principal dimension of the radiator but radio waves may behave differently in the near field as unlike light or radionuclide emissions from a practical source, the wavelength  is commensurate with the radiator.

[hamdani yusuf]

Furthermore, an electric charge moving in constant velocity also generate electromagnetic field.

No. A charge moving at constant speed generates a magnetic field, and the charge itself has an electric field, but there is no radiative EM field. This goes right back to Isaac Newton! 

The magnetic field changes in any stationary position, which is moving wrt the moving charged particle. The changing magnetic field generates electric field.