Oscillation coil: where is the electric field? Let assume a simple RF coil fed with an alternating current at RF frequencies, say 100MHz.
I believe that no one doubts that the coil will radiate RF energy in the form of radio waves.
A radio wave is classically composed of an electric vector and a magnetic vector orthogonal one to the other.
Now, let assume a low frequency big coil, say, for magnetic induction, and assume it is fed by a low frequency current (e.g. 1 KHz). An oscillating magnetic field will be perceived near the coil, but I've never heard that the coil also radiates a sensible electric field. Yet, there is no difference with the former RF coil, but the frequency. So, my question is: why is there no sensible electric field radiated by the low frequency coil?
 A: One has to distinguish the near field (i.e., the field near the coil) and the far field, i.e., the propagating electromagnetic waves far away from the coil (far away on the scale of the wave length). The major factors that determine whether the oscillating electric current will produce a propagating electromagnetic wave are:

*

*the damping should be weak

*the energy of the electromagnetic wave should be substantial to be detected and to be of interest for practical applications (otherwise you will never hear about it).

Kilohertz frequency waves have wave lengths of several hundred kilometers - too long to be of practical use, and even to be generated by conventional methods (which typically require an antenna of half-wave length size). Yet, such waves are known to exist in the atmosphere and can be rather easily detected (to the extent that in some universities their detection is a subject of an undergraduate lab experiments). They go under the name of whistlers.
A: Since the magnetic field is varying with time, by Maxwell-Faraday's induction law there is a rotation of the electric field. One can then distinguish the propagating and the non-propagating part but that is outside the scope of the question.
A: There is no fundamental difference between 1 kHz, 100kHz or higher frequencies. RF coil may radiate a lot or very little (see magnetic resonance imaging), it depends on how the coil is used.
Oscillating current always produces some waves, but whether it is useful or strong enough for some purpose depends on details. Two of those details are 1) EM wave strength, 2) ease of propagation, 3) information throughput. 1),3) get better with increasing frequency, but 2) gets worse. So some finite frequency windows are used for different uses.
As a general rule of thumb, assuming fixed current amplitude, the higher is the frequency, the higher the amplitude of emitted waves. This is because the higher the frequency, the greater is the acceleration of mobile charges which is what produces electric and magnetic field of EM waves.
Also, with higher frequency information throughput is better because of larger frequency bandwidth available. But too high frequencies propagate badly over obstacles and over long distances, they cannot use ionosphere reflections for long distance propagation, they do not penetrate seawater well etc. So one can't just use GHz or higher frequencies for everything. Along Earth's surface lower frequencies <GHz propagate better.
If the frequency gets very low, radiation intensity of a given emitter gets very low as well and is easily drowned by EM noise, so it is not very common to encounter kHz or slower transmitters/receivers. It is possible to run such low frequency transmitters but to make them effective requires that they are very big (comparable to radiation wavelength). One well known example is the VLF communication with submarines which uses many kilometer long antennae.
https://en.wikipedia.org/wiki/Very_low_frequency
