Illustrated Physics
physics, drawn
Concept

Shielding — where it appears

Reducing a field inside a region by surrounding it with material that responds to the field. Conductors shield electric fields and high-permeability metals or superconductors magnetic ones, and how well it works depends on the frequency and on whether the shield is closed.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Skin depth against frequency, over eleven decades. The skin depth of copper, stainless steel, seawater, mu-metal against frequency, both axes logarithmic. Every line has the same slope, −½, because the depth goes as the inverse square root of the frequency for all of them; what separates them is conductivity and permeability, which enter the same way. Three points are marked and each is a practical fact. Copper at mains frequency has a skin depth of 9.22 mm, so a busbar of that thickness carries current throughout and a thicker one does not. Copper at a gigahertz has 2.1 µm, so the current in a microwave component runs in a layer thinner than the plating and the surface finish becomes the conductor. Seawater at the frequency navies use to signal submerged submarines has 28.9 m, which is why that link is measured in tens of hertz and carries a few characters a minute. Mu-metal is the outlier and the reason it exists: its conductivity is forty times worse than copper's and its permeability twenty thousand times better, so at low frequency it is the one material on the chart that is thin.

How far a field gets into metal

Every static argument about conductors says the field inside one is zero, and every one assumes the electrons have had time to move. Give them less time and the field gets in — 9.2 millimetres into copper at mains frequency, 2.1 microns at a gigahertz — and the metal box that silences a radio does almost nothing about the cable running past it.

electromagnetism · Conductors A cage of wires in a uniform field. Equipotential lines round a cage of 12 parallel wires, each 2 per cent of the spacing in radius, joined so that they share one potential and carry no net charge, in a uniform field running left to right. Outside, the lines bunch and bend round the cage as they would round a solid cylinder. Inside, they do not vanish: they run straight across, carrying a uniform field 25.8 per cent as strong as the one outside (dashed, drawn at a fifth of the outside spacing because the potential differences inside are so much smaller). The wires' charges are computed so that every wire is at the same potential.

The field a ring of wires lets through

A cage made of wires is supposed to work almost as well as a solid box, because the field that leaks through the gaps dies away exponentially within a gap's width. The exponential is real and it is the wrong part of the story. It describes the ripple the separate wires make; underneath it the average field goes straight through, at a level that falls only in proportion to the spacing and depends on the wires' thickness through a logarithm. A cage of twelve thin wires lets a quarter of the field in.

electromagnetism · Potential

Named alongside it

The objects these essays reach for when they reach for this one.

ConductorsConductivityDiffusionEddy currentsElectric potentialThe Faraday cageFourier seriesLaplace equationPermeabilityProximity effectSkin depthSurface charge

All concepts