Electromagnetic waves are produced by the motion of a dipole and suppose we have top and bottom points then the negative and positive charges must oscillate between those 2 points.
However an LC oscillator does exactly the same thing if you consider the poles to be each conductive plate of the capacitor.
Are electromagnetic waves produced during the oscillation of charge in a LC oscillator?
Consider a disk capacitor "shorted" with an external loop. Even if the external loop has no resistance, there is some inductance associated with the loop, and therefore the discharge can lead to an oscillation at a frequency determined by the inductance and capacitance of this structure. If this loop is sufficiently large compared to the free space wavelength at the frequency of this oscillation, the loop will radiate appreciably as a magnetic dipole, with a sizable radiation resistance. - thanks to R. C. Levine, "Apparent Nonconservation of Energy in the Discharge of an Ideal Capacitor," in IEEE Transactions on Education, vol. 10, no. 4, pp. 197-202, Dec. 1967, doi: 10.1109/TE.1967.4320288.
Actually, an LC tank (as part of a functioning LC oscillator) will produce a near field electromagnetic field around the inductor as alternating currents move through it. However this won’t be suitable for long distance transmission of electromagnetic waves to a receiver. It can be used for close transmission as similar to transformer operation.
For long distance transmission, you could use an LC oscillator circuit to create alternating current, and feed it to an antenna such as a dipole antenna. Here the antenna would help direct the waves in a certain direction and give optimal radiation when antenna is sized based on the frequency of signal.
Let's assume you connect a charged capacitor and an inductor in parallel the circuit starts to oscillate. There's a sinusoidal electric field between the ends of the coil and that's enough for creating electromagnetic radiation. The radiation power can be quite small in practical LC circuits when compared to the power of the energy transfer between the capacitor and inductor, but it's not zero. The oscillation decays fast due the resistance of the coil if you do not have an oscillator circuit with an amplifier which sustains the oscillation.
LC circuit would be useless if the radiation power was substantial, because losses would destroy the narrow bandwidth property of the circuit. The amount of the radiation depends on how big are the parts of the circuit and how long connection wires are used when compared to the wavelength. There's no strict limit, but radio builders try to keep the dimensions less than 10% of the wavelength, preferably only 1% or even less. In microwave circuits this is not possible, so there LC resonators are ineffective and the wiring must be designed as transmission lines.
If you take an ordinary FM receiver (88-108MHz) you find with another FM receiver how its local oscillator (=LC transistor oscillator) radiates. The signal can detected from 10 meters or even further.
Are electromagnetic waves produced during the oscillation of charge in a LC oscillator?
Yes, and this is a fascinating niche-topic in antenna-design, called "electrically-short resonant antennas." If a coil/capacitor is far smaller than quarter-wavelength, it's still able to become a "virtual antenna" which behaves as if it was greatly larger than its physical size. Go look up "ceramic chip antennas" currently used in many phones and tablets.
For example, in oldschool AM pocket radios, the antenna is not just a pickup-coil; not only a ferrite rod-inductor. In addition, the tuning capacitor for the superhet local-oscillator has a second floating variable capacictor section. It's always connected across that inductor. The little coil is tuned to resonance at the AM station being received, and this immensely increases its EA Effective Aperture (or Effective reception Area.) Yet the 4cm "ferrite dipole" could be operating at 550KHz, a wavelength 6800X longer than 4cm.
Very weird. Why does resonance make tiny antennas "become larger?" How does antenna-EA work?
Both for reception and transmission, if a tiny antenna is operating at resonance, then its surrounding fields will be much stronger than at other frequencies. Strong fields will radiate more EM. In theory, if the Q-factor of the resonator is enormous, then even for low drive signals, the small resonator can almost approach the same emission as a half-wave dipole antenna! (Just use some superconducting metals for your coil and capacitor.) Then, with zero resistive-loss at resonance, the V and I (and the surrounding fields) will go to infinity ...or at least grow so large that the "EM leakage" dominates the behavior. In that case the resonator's effective resistance becomes significant, even when the resistance of the entire circuit is zero. The oscillator has started "seeing" the wave-impedance of the surrounding empty space. Same as using a half-wave dipole antenna where the antenna is 75 ohms, yet the wire itself is only 0.1 ohms.
So, whenever our tiny RLC tank-circuit has extremely low resistance (employing low-loss dielectric, multiple parallel windings/Litz-wire, perhaps air-core coil and vacuum capacitor,) then at resonance we've optimized the "unwanted RF leakage," and our circuit has become a very significant antenna. And, whatever works for emission, also works for reception. A small incoming RF signal will build up to unlimited V and I within the resonator ...or at least rise until the microwatts lost to the receiver's input-impedance is the same as the microwatts absorbed from incoming EM waves.
For some reason this topic has been controversial in electrical engineering! It's well-known in physics. But oddly will make many EEs angry, and in the past has led to actual online flame-wars. (The topic wasn't in our textbooks? Then we simply refuse to believe that it's real!! And even worse, it means that Nikola Tesla may have been right all along!!! Heh.)
Win Hill, author of "Art of Electronics" suggests these papers to convince unbelievers:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.70.035418
https://aip.scitation.org/doi/abs/10.1063/1.1512691
Earlier, people on SED newsgroup found this one from 1948: https://aip.scitation.org/doi/abs/10.1063/1.1715038
Here's my take on it: small RLC antennas operating at resonance
And here's an entire book on the math: Absorption and Scattering of Light by Small Particles Bohren & Huffman 1983
Weirdest of all ...this is how atoms can efficiently emit waves. A particular atom is roughly 0.1nM wide, yet perhaps it strongly absorbs/emits red light at 700nM. That's like having a 1MHz radio antenna that's two centimeters long! 3e10/1e6/2/700/0.1 = 2.14cm
Single atoms behave like very small RLC tank-circuits having very large Q-factor (where the tiny linewidth of the atomic emission-line is inversely proportional to the "Q" of the atom-circuit.) Single atoms are like little bitty LC oscillators where the antenna can be roughly 10,000X smaller than the operating wavelength.
In other words, resonant RLC oscillators, as well as the ceramic chip-antennas inside our phones, start "emitting photons" in the basically same way that atoms do! (Just wow!)
In the above, if R2 is made extremely large, then for ideal lossless components, the main circuit-resistance becomes the impedance of free space, and the circuit "leaks" the same amount of RF as a half-wave dipole antenna.
Maddy --- an antenna produces 3 different emissions.
There is the radiative field, and two reactive fields.
This per Corson and Larraine book. And wikipedia "near and far fields"
Close to the antenna, the two reactive emissions are very strong. But their rate of dropoff is very fast, so eventually (about a wavelength away) the third form of emission has become the strongest.
So there is a lot going on around an "antenna".
I recall an article decades ago in Wireless World (from which I learned much about interesting precision circuits; see if you can find old issues of WW) on using an inductor and some parallel metal plates (capacitor) to generate a standard radiation pattern.
The mail from the readers was strenuously flowing, and strenuously worded.
Eventually people were able to explain ----- this does not happen.
The inductor and capacitor are not able to create the photons needed for genuine radiation like an antenna does.
