Faraday cage
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A Faraday cage is really any object made of a conducting material that is hollow in some manner. The laws that govern our understanding of electricity and magnetism state that "for any object made of a conducting material, the electric field at any point inside that object is zero" The same law mentions other things (like the field being normal to the outside of the object at any point) but really the only thing you need to know is that you can't get shocked if you are inside a Faraday cage while it is being zapped.
Pretty much the easiest demonstration of a Faraday cage would be an elevator car.
Practical applications
Placing a grounded wire mesh into the walls of a building provides a secure environment for computers where it is impossible to read the signals from a keyboard remotely. Radio and mobile telephone are also unusable.
The cooking area of a microwave oven is surrounded by a Faraday cage. This keeps nearly all of the microwave radiation from escaping. It's also why there's that annoying metal grid in the glass door which makes it harder to see your food.
When you're on call, keep your phone in easy hearing range and safe from harm! The microwave is a particularly safe place and protects it from incoming calls too.
Faraday cages are actually woven into the clothes of some power linemen, especially the "hot hands" variety (This means they work on live power lines without special insulating tools) and this allows them to perform maintenance on live power lines without the need to shut off power. Theoretically speaking, these suits would allow the lineman to take an infinite amount of current and suffer no harm, although practically speaking the suit would burn after a certain point.
Source of confusion
The best material for a Faraday cage is highly conductive (of electricity, not heat). So silver or copper if money is no object, aluminum for the econo lab (presumably aluminium only works in the UK). Lead is not suitable, although it is weakly conductive. Lead linings in e.g. hospital radiology labs are a quite different thing. They are for screening ionizing radiation, not radio waves. In this case the preferred material has high density, and its conductivity is a secondary consideration. So when, for example, Mike Bara wrote on page 139 of The Choice that Faraday cages are made of lead he was, as usual, wrong.
Origins
The first Faraday cage was made in 1836 by Michael Faraday, a highly influential scientist largely responsible for making electricity a viable technology[1]. It was quite a simple design; a room covered in metal foil in order to allow high-voltage discharges from a generator that would hit the outside of the room without harming anyone or anything inside.[2]