The arc has been promising this: why the inside goes exactly to zero. The shell's charges rearrange until the field lines from outside end on the surface and never make it in. Here's the mechanism, drawn — and where it gets subtle.
The shell's free charges slide to the surface, repelled and attracted by the outside field.
slides to skinThat surface charge makes its own field that exactly opposes the outside one within.
exact oppositeExternal lines terminate on the surface charge; none cross into the cavity.
end on surfaceStatic is perfect; waves bring skin depth, mesh size, and apertures into play.
it dependsThe outside field pushes the shell's free charges until one face is negative and the other positive. Their field exactly opposes the external one inside the metal and the cavity, so every external line ends on the surface — and the interior is left at zero. Move charge around outside and the surface charge re-arranges to keep cancelling it.
A conductor's electrons are free to roam — that's what makes it a conductor.
fact mobile charge inside the metal
so any field that reaches them pushes them until they stop reaching equilibrium.
+1 an insulator can't do this — its charges are stuck, so a plastic box is a poor cage.
Charges keep sliding as long as any field pushes them — and stop only when none does.
rule equilibrium = no net force
so the field inside the metal settles to exactly zero.
+1 "exactly" is forced: any residual field would still be moving charges, contradicting equilibrium.
Electric field lines start and stop on charges — and the induced surface charge catches them.
rule lines terminate on charge
so outside lines die on the surface; none thread the cavity.
+1 this is Gauss's law in disguise — no enclosed charge in the cavity means no net flux through it.
With no field and no charge inside, the hollow is electrically dead.
result E = 0 in the cavity
so anything inside is shielded from the outside field.
+1 it holds for any cavity shape — the shell needn't be a sphere to work.
For steady fields, a closed conductor is a flawless shield — zero inside, full stop.
case electrostatics
so the No. 0 picture is exact: total cancellation.
+1 the textbook "perfect" cage is the static case — everything subtle comes from things changing.
A changing field induces currents that live in a thin surface layer.
term skin depth
so even a thin metal skin shields well — the action is all at the surface.
+1 higher frequency = shallower skin depth, so high-frequency RF is actually easier to block than low.
A wave only leaks through an opening comparable to its wavelength.
rule hole ≪ wavelength = blocked
so mesh blocks long waves and passes the very short (like light).
+1 it's the long, low-frequency waves that sneak through mesh — the opposite of many people's guess.
A slot can resonate and leak badly near a matching wavelength.
watch long seams and slots
so a thin gap can leak far more than a round hole of equal area.
+1 this is why No. 1 said "close slots first" — a resonant slot is an antenna cut into your shield.
A static magnetic field passes straight through — the cage doesn't touch it.
why no magnetic "charge" for lines to end on
so a magnet still pulls through foil and mesh.
+1 blocking static magnetism needs a high-permeability metal (mu-metal) that guides the field around — a different mechanism entirely.
Slowly-changing magnetic fields are hard to shield with a plain conductor.
case mains-frequency magnetic hum
so you need thick conductors, mu-metal, or distance.
+1 this is why twisted pairs (No. 2) exist — to cancel magnetic pickup the cage can't stop.
Perfect conductors are ideal; real metal has resistance and finite thickness.
reality finite conductivity
so shielding is excellent but not literally infinite — rated in dB.
+1 "perfect inside is zero" is the idealization; real cages get 40–100+ dB, which is plenty.
The same cancellation keeps inside fields from getting out.
symmetry shielding is reciprocal
so a cage contains emissions as well as it blocks them.
+1 that reciprocity is why one screened room serves both "keep out" (MRI) and "keep in" (secure) jobs.
workbench series · no. 3 · lines end on the surface, the inside stays quiet · except magnetism, and except the gaps