How a dipole should behave in order to produce an electromagnetic field? I am trying to understand what an electric dipole "has to do" to produce electromagnetic waves. I know that an oscillating electric dipole will produce EM waves and by oscillating electric dipole I mean two opposite charges $q$ that move with an harmonic motion approaching each other;
I also know that this is possible since every time we have a time-varying electric field or a time-varying magnetic field we see from Maxwell's equations that EM waves are produced so, back to the oscillating dipole, of course it will produce a time-varying electric field.
Now, hoping I have said everything right so far (let me know), the doubt:
I've read about Hertz's oscillator and that this kind of "oscillating" dipole can be reproduced with an RC circuit in AC current. What does it happen in an RC circuit in AC current? It happens that the capacitor's armatures will charge with a positive charge that will go from $0$ to a certain positive charge $q$, consequently the other armature will charge with a negative charge from $0$ to the same amount of charge $-q$;
then the current will change direction so that the first armature will lose gradually the positive charge $q$ unloading completely and will recharge with negative charge $-q$ and so will do the second armatur in the opposite way.
What we get with this circuit is: two areas in the space separated by a certain distance $d$, the distance between capacitor's armatures, which periodically have a positive charge and a negative charge that grow, decrease by passing through $0$, grow in the opposite direction decrease by passing through $0$ and so on.
So physically we have two different situations if in a laboratory we have an RC circuit in AC current or two opposite charges oscillating (like an atom in an EM field) that act in the same ways if we look at EM waves they produce.
And here is my point:
The definition I know of an electric dipole is:An electric dipole is a pair of equal and opposite point charges $-q$ and $q$ separated by a distance $d$, so whenever I look at the armatures of the capacitor I see a dipole but not an oscillating dipole since the distance $d$ is a constant, so we are producing EM waves without an oscillating dipole. Is it possible?
1. Is this system actually an oscillating dipole or is it simply a model that behaves as one?
2. This circuit produces EM waves since it is actually an oscillating dipole or in general because every time we have a time-varying electric field or a time-varying magnetic field we see from Maxwell's equations that EM waves are produced? and this is just a realistic and simple way to emulate an oscillating dipole but actually not properly an oscillating dipole?
 A: Suppose you had a dipole with a constant distance d between the equal charges, and the dipole rotated.
Then the charges would be accelerated and it would produce EM waves.
The EM waves would be linearly polarized in the plane of rotation, and would be circularly polarized normal to that plane.
So I don't see any problem if you choose to call a capacitor a dipole, and think of it as oscillating. Why not?
A: As long as the dipole moment (a vector quantity) oscillates, the system radiates. If you know how the dipole moment changes with time, that's enough. The reason why the dipole moment changes doesn't matter. Radiation will be emitted.
There are actually only two ways in which the dipole moment can change. Either charged particles can move, which changes the displacement vectors between them and therefore the dipole moment. (If they manage to do a dance where the total dipole moment doesn't change, then radiation might not be emitted, although there is still the possibility of radiation from the quadrupole or higher moments.)  Or, fundamental dipoles (and we are not sure whether any actually exist in nature) can rotate, changing the directions of their dipole moments.
Your scenario, involving an oscillating circuit, is actually the same scenario as oppositely charged particles oscillating; it just has more particles! The only way that one plate can become positively charged while the other becomes negatively charged is by the movement of negatively charged particles from the former to the latter, or the movement of positively charged particles from the latter to the former. A charge separation builds up, where none previously existed, because of the movement of charge carriers. This gives the capacitor a dipole moment. When the capacitor discharges, it is because the charge separation is winding down. Fundamentally, there isn't much difference between this and a single pair of oppositely charged particles that initially move away from each other, then toward each other.
A: Suppose you have a dipole moment consisting of two charges $\pm q$ and the length between them is $d$. But now suppose that the charge at "each end" of the dipole is time dependent such that $q = q_0 \sin \omega t$, then the dipole moment is
$$ p = q_0d \sin \omega t$$
But current is $dq/dt$, so
$$ I = \omega q_0 \cos\omega t = I_0 \cos \omega t\ ,$$
where we have now defined $I$ to be an AC current with amplitude $I_0 = \omega q_0$.
Using this definition, we can see that the electic dipole moment could be written as
$$ p = \frac{I_0 d}{\omega} \sin \omega t \ . $$
Thus the two situations are entirely equivalent, with the electric dipole moment amplitude replaced by $I_{0}d/\omega$ and the oscillating AC current produces an oscillating electric dipole moment.
