[tgb]

Interesting results. The article states that Faraday cages are no directional. My physics 101 understanding of them was otherwise. You show they work by integrating over the surface of the cage and saying that's equal to the charge within the surface. But you don't say it's equal to the charge outside. Indeed it couldn't possible, since that charge could be light-years away and steady state would never be achieved. Now that was for electrostatic which isn't really what we care about, if I remember correctly.

Wikipedia also states they are more effective at blocking incoming than outgoing signals. Can anyone clarify the situation?

[Johnythree]

Building an effective Faraday Screen is surprisingly difficult:

There are three completely different scenarios, blocking electrostatic fields, blocking RF energy, and blocking alternating magnetic fields.

The first can be achieved by a thin conductive screen (eg brass mesh with soldered seams), the second by thick copper sheet (with bolted seams) and the third requires thick magnetic material (eg iron or nu-metal).

[pfortuny]

If you consider the compactification of R^3 by a single point “at infinity”, an electric charge inside the surface is the same as the opposite charge at infinity (this is just Gauss’ result). In that sense, “infinity” acts as the opposite charge, does it not?

I do not understand your question, otherwise.

(Not a criticism, just an interested comment which may be very wrong though).

[posix_me_less]

> If you consider the compactification of R^3 by a single point “at infinity”, an electric charge inside the surface is the same as the opposite charge at infinity (this is just Gauss’ result)

This is a mental operation, not physically possible. The difference is real: for example, charge inside a perfect conductor cavity generates electrostatic field outside. A charge outside perfect conductor cavity does not generate any static field inside.

[tgb]

This is what I wondered about back in physics class. Does that prove the universe is not compact? If it were, then inside-outside is the same. But surely that's not enough to know the shape of the universe. My 'resolution' of this was to say that the universe is surely very large and so the time to reach equilibrium will be very very long. So the experiment cannot really be run to completion.

But would a point charge outside a conductor cavity ever come to equilibrium where it does generate an electric field inside the conductor cavity? Assuming compact but very large universe. It seems strange but I guess it would.

[pfortuny]

Aaaahhhhh!!!!

Thank you for this comment, truly enlightening (I am a mathematician and know 0 physics). Shall have to think about it.