I read this statement in Feynman Lecture on Physics (see here for more details):
In low-frequency circuits the connection is made with wires, but this method doesn’t work very well at high frequencies because the circuits would radiate energy into all the space around them, and it is hard to control where the energy will go. The fields spread out around the wires; the currents and voltages are not “guided” very well by the wires.
I read this statement many times but I do not have in mind the physical (why the electromagnetic field goes "far" from the circuit) and also the mathematical reason of this (I image there should be a frequency dependence on some parameters which defines the "irradiation"). Why, given a certain circuit, high frequency means irradiation?