So far-field makes intuitive sense to me, it attenuates at $\frac{1}{r^2}$ much like gravity. This is just common sense since the area for the surface of a sphere relative to its radius has a $r^2$ relationship.
However the near-field attenuates at a rate of $\frac{1}{r^6}$ instead. Is there some equally intuitive explanation for this? How is this derived?
The above numbers can be confirmed from the following Wikipedia article. To quote the article:
According to Maxwell's equation for a radiating wire, the power density of far-field transmissions attenuates or rolls off at a rate proportional to the inverse of the range to the second power ($\frac{1}{r^2}$) or −20 dB per decade. This slow attenuation over distance allows far-field transmissions to communicate effectively over a long range. The properties that make long range communication possible are a disadvantage for short range communication systems.
NFMI systems are designed to contain transmission energy within the localized magnetic field. This magnetic field energy resonates around the communication system, but does not radiate into free space. This type of transmission is referred to as "near-field." The power density of near-field transmissions is extremely restrictive and attenuates or rolls off at a rate proportional to the inverse of the range to the sixth power ($\frac{1}{r^6}$) or −60 dB per decade.
