[hamdani yusuf (OP)]

If a bar magnet or an electric dipole is not moving, their field strength decrease with distance according to inverse cubic law. When they are rotating very slowly, say 1 rpm, the field strength compared to distance doesn't seem to change much, which means it's still following inverse cubic law. But if the fequency is very high, like in a light bulb, the radiation seems to switch to inverse square law. How does this happen?

[evan_au]

When [magnets] are rotating very slowly, say 1 rpm...

In my basic understanding of Maxwell's equations, the strength of an electric field increases as the rate of change of the magnetic field increases (and vice-versa).

At 1 Revolution Per Minute, the magnetic field is changing very slowly, so the electric field will be very weak. This means that any electromagnetic radiation (which follows the inverse square law) will also be very weak, and hard to detect.

Even worse, the wavelength of the electromagnetic radiation will be 60 light-seconds, so:
- To detect it efficiently, you need an antenna many times the diameter of the Moon's orbit around the Earth
- To get past the near-field effect, you need to position this antenna many wavelengths away from the source - say, at the orbit or Mars.
- And you have no chance of detecting anything in the presence of all other radiation sources from Earth, Mars, and thunderstorms on Jupiter...

If you want to measure the transition from near-field to far-field in a practical way, do it faster and closer:
- Use 300MHz frequency, where the wavelength is a meter
- Feed this into a coil antenna
- Measure the intensity with another coil antenna, moving it from adjacent to hundreds of meters away
- You need to move the receiving coil away from the source by several times the diameter before you have a chance of detecting the radiated signal.

Note: Consider this a thought experiment; people who transmit radio interference that obliterates licensed spectrum users (potentially including essential services like aircraft and emergency services) are not appreciated by the authorities!

[hamdani yusuf (OP)]

In my basic understanding of Maxwell's equations, the strength of an electric field increases as the rate of change of the magnetic field increases (and vice-versa).

At 1 Revolution Per Minute, the magnetic field is changing very slowly, so the electric field will be very weak. This means that any electromagnetic radiation (which follows the inverse square law) will also be very weak, and hard to detect.

Even worse, the wavelength of the electromagnetic radiation will be 60 light-seconds, so:
- To detect it efficiently, you need an antenna many times the diameter of the Moon's orbit around the Earth
- To get past the near-field effect, you need to position this antenna many wavelengths away from the source - say, at the orbit or Mars.
- And you have no chance of detecting anything in the presence of all other radiation sources from Earth, Mars, and thunderstorms on Jupiter...

If you want to measure the transition from near-field to far-field in a practical way, do it faster and closer:
- Use 300MHz frequency, where the wavelength is a meter
- Feed this into a coil antenna
- Measure the intensity with another coil antenna, moving it from adjacent to hundreds of meters away
- You need to move the receiving coil away from the source by several times the diameter before you have a chance of detecting the radiated signal.

Note: Consider this a thought experiment; people who transmit radio interference that obliterates licensed spectrum users (potentially including essential services like aircraft and emergency services) are not appreciated by the authorities!

I'm aware of your concerns above.
I suspect that the field strength's transition from inverse cube to inverse square of the distance is due to the movement of electric charges. What I want to know is the mechanism behind the emergence of that transtition.

[hamdani yusuf (OP)]

I found an answer from quora explaining transition from near field to far field radiation. Perhaps we can relate this to the question in this thread.

Why antenna radiates?

Subra Ananthakrishnan, Adjunct Professor, Pune University
Answered May 2, 2017
—

One of the least understood phenomena in electrical engineering is the idea that electric and magnetic fields appear to leave a radio transmitting antenna to form what we know as radio waves.

For a time varying current, we can write dI/dt = ql dv/dt =ql a,

, where a is acceleration. This basic relation means that to create radiation, there must be a time-varying current or an acceleration /deceleration of charge. There are three fields associated with the antenna. The static field, the Near Field (reactive or stored), and the Far Field (the radiated portion) as a result of acceleration and deceleration of charges.

The Near Field (stored) can be stated as follows:
 If there is an alternating current in a conductor, an alternating magnetic field will be created surrounding the wire. The alternating magnetic field due to the current in the wire will create an alternating electric field in space further out from the conductor. The first transition from conduction fields to near fields has been made.

Now, carrying it further, the alternating electric field, will create a magnetic (due to the corresponding displacement current in space) field further away from the conductor.

The alternating magnetic field will then create another alternating electric field. This process, which continues on away from the conductor is called electromagnetic wave propagation. Why are the fields in quadrature close to an electrically small antenna and in phase far away?

You have heard of the Poynting flux (E X H), which is the measure of the energy flux around the hypothetically small antenna. If the electric and magnetic fields are in phase quadrature, then half the time the fields have the same sign and half the time the fields have opposite signs. Thus half the time the Poyn. Vec. is positive (outward flow) and half the time it is negative (inward flow). This is the imaginary power or reactive power in the near field.

In the other case, both electric field and magnetic fields are in phase and so when one is positive the other is also positive and in both cases it is a positive Poyn. Flux which means there is an outward flow of energy. This is the far filed. Thus there is smooth transition from Near field to Far field when an antenna radiates.

These concepts have their mathematical equivalence via Maxwell’s equations. If we look at the E (theta) field at a distance r, then one can see a radiation term and an induction term. The induction (reactive)term vanishes farther away from the antenna and the phase smoothly transitions from a quadrature to in-phase. That is how radiation takes place.

(put together for ease of understanding – from various websites by unknown authors)