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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?

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    $\begingroup$ look up "waveguide" on wikipedia. $\endgroup$ – niels nielsen Sep 20 '19 at 6:54
  • $\begingroup$ Imagine high frequency irradiation in W/m2 by solar shining. You, Sun and space also form a kind of high frequency circuit. The similar for microwave ovens. $\endgroup$ – Poutnik Sep 20 '19 at 7:15
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The antenna in a radio transmitter or receiver is basically just a piece of wire. OK, the wire is usually made into a special shape, but that is just to make it more efficient.

Every piece of wire in a physical circuit acts like an antenna and picks up some of the EM field radiated from every other piece of wire.

At low frequencies this effect is too small to interfere with the way the circuit is intended to work, but at high frequencies it becomes more important.

These effects become critical when "wires" are longer than about 10% of the wavelength of the EM radiation. For computers and cellphones operating at frequencies of a few GHz, the wavelength is the order of 100mm so any "wire connection" more than 10mm long can act as a transmitting or receiving antenna.

These issues are overcome by careful design of the physical layout of the connections, and "shielding" conductors from each other by placing another conductor between them to absorb the unwanted EM radiation. Reducing the size of the device also helps, by making all the interconnecting "wires" shorter - devices like cellphones need to be small in order to work at all, not just to make them easier to carry about!

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