Faraday cage

Why does a metal mesh you can see straight through block a radio signal almost completely?

The window of a microwave oven has a metal sheet perforated with holes a millimetre or two across. You look straight through it and watch your dinner turn. Yet the microwaves, which would cook your hand, do not come out.

The instinct is that the metal must be absorbing them, and that the holes are somehow too small for the radiation to fit through. Both halves of that instinct are wrong in interesting ways. So what is the metal actually doing — and what is it about the holes that matters, if not their being physically narrow?

Start with the metal, and with no radiation at all — just a steady external electric field and a lump of conductor sitting in it. A conductor is defined by having charges free to move. The field pushes them; they move; they pile up on the surfaces. Do they stop? Only when the field they themselves produce inside the metal exactly cancels the applied one. If any field remained, charges would still be feeling a force, and they would still be moving. So equilibrium means zero field inside the conducting material. Nothing else is stable.

Now hollow it out. Inside the cavity there is no metal and no free charge, so what forbids a field there? The argument is a little sharper and worth following. Every point of the shell sits at the same potential, since no field inside the metal means no potential difference along it. The cavity is therefore a region bounded entirely by a surface at one fixed potential, containing no charge — and the potential in such a region cannot have a peak or a trough inside it, so it must be that same constant throughout. Constant potential, no field. The screening is not partial. It is exact, and it follows from the boundary being closed and conducting, not from the walls being thick.

That handles a static field. What about a wave? Now the external field oscillates, and so do the surface charges — they slosh back and forth, which is to say they form currents, and accelerating charge radiates. The re-radiated wave from those induced currents is what cancels the incoming one behind the sheet. The metal is not a sponge soaking up energy; it is a mirror, and the energy it does not let past is mostly sent back the way it came.

And the holes? Here is the point the microwave door makes so cleanly. The surface currents only need to keep flowing; an aperture matters when it forces them to detour badly, and that depends on the hole's size compared with the wavelength, not on its size in absolute terms. Bethe's analysis of a small hole in a conducting screen gives a transmitted power falling as the fourth power of the ratio of hole size to wavelength — a recalled result, but the steepness is the whole story. Microwaves in an oven are at 2.45 GHz, so their wavelength is 3 × 10⁸ divided by 2.45 × 10⁹, about 12 cm. A 2 mm hole is a sixtieth of that, and a sixtieth to the fourth power is around a ten-millionth. Visible light has a wavelength near half a micrometre, so the same hole is thousands of wavelengths wide, and light strolls through as if the sheet were not there. One screen, two utterly different verdicts, from one ratio.

Three honest complications, each of which is a real limit people run into.

The screening is one-directional in the electrostatic case. A closed shell perfectly shields its cavity from outside charges. But a charge placed inside pulls an equal and opposite charge onto the inner surface, leaving its counterpart on the outer surface — and that outer charge produces a field outside. Unless the shell is earthed, so that charge can drain away, an enclosed source is still felt from outside. The cage is far better at keeping fields out than in.

Static and slowly varying magnetic fields largely pass. Nothing in the argument above applies to them: a copper shell has no magnetic charges to rearrange, and cancellation by eddy currents requires the field to be changing fast enough, and the wall thick enough relative to the skin depth, for those currents to be substantial. A compass inside a wire cage still points north. Shielding a steady magnetic field takes a high-permeability alloy that diverts the flux instead, which is a different mechanism entirely.

And the enclosure must genuinely be an enclosure. A long slot is far worse than a round hole of the same area, because it forces a longer detour on the surface currents; seams, hinges and cable entries are where real shielded rooms leak.

The test that would refute all this: build two cages of identical metal mass, one with 1 mm holes and one with a 15 cm gap, and put a 2.4 GHz transmitter inside each. The mesh picture predicts the fine one blocks the signal and the coarse one barely does, despite equal metal. If instead shielding tracked the mass or thickness of metal and ignored hole size, the induced-current account would be wrong — and if a compass inside the sealed fine cage swung away from north, the claim that static magnetic fields pass would be wrong too.

• Why skin depth sets how thick a shield must be, and why it shrinks as frequency rises.
• How a car protects occupants from lightning, and why the danger there is the current in the shell rather than the field inside it.

Every term the collection defines is gathered in the glossary.