Capacitor electromagnetic radiation

Question

The plate capacitor is charged and discharged with sinusoidally changing electric current. Why does a capacitor emit electromagnetic radiation?

Answer 1

A charged particle possesses an electric field and a moving charged particle produces as magnetic field. Charging (and also discharging) the capacitor sinusoidally accelerates the charged particles with a certain frequency $\nu$. This leads to emission of electro-magnetic radiation of energy $E = h \nu$, as the produced magnetic and electric fields caused by the charged particle vary over time. An electro-magnetic wave is nothing else than a temporal and spatial variation of electric and magnetic fields.

For further reads see here, here and here .

Answer 2

What we define radiation is a component of the EM field caused by an accelerating charge.

For a capacitor discharging sinusoidally

$\frac{\partial \vec{J}}{\partial t} ≠ 0$

Meaning there is radiation.

See: https://en.m.wikipedia.org/wiki/Jefimenko's_equations