Gauss' Law and the Faraday Cage

[ExileStrife]

The whole "electricity chooses the path of least resistance" is a fallacy.  Electricity doesn't completely "ignore" a path to ground just because there is another path with lower resistance.  Current travels through everything that's connected to the system -- the majority will go through something with low resistance (like steel) compared to something with high resistance (a body), but that doesn't mean there's no danger involved!  It only takes a low amperage to fuck a body up, and you'd certainly be meeting those numbers from a megavolt or greater source (like a lightning bolt) despite there being another material in the system with a low, low resistance.

Come on, let's throw math and physics aside for a second and think.  If somebody gave you the opportunity to put on a metal suit and walk out into a open field during a lightning storm, would you?  No!  Not only would you die from the straight up current though your body we've been discussing, but you would literally ~fry~ as the temperature of that much current flowing through both your body and the steel heats both of those up to temperatures that ~melt~ steel.

If you want to have an insulating suit/faraday cage, you need a substantial insulator between you and the conducting material.  And don't skimp on the material, since perfect insulators don't exist!  Now, we'd not longer be talking about fullplate, but instead it would be fullplate with thick, thick layers of leather lining the inside making it impossible to function.

[Thomas_Not_very_wise]

This is madness.

[Pup]

ExileStrife is right on the money.

[Archon]

This is madness.

This is SPARTA!

[Thomas_Not_very_wise]

This is SPARTA!

Kekekee

[Relinquish]

NWN =/= Real Life.

It obeys gravity and that's about the extent of it.

[ScottyB]

More importantly, NWN is a game, and there's no reason to throw off the mechanical balance of every electrical spell / suit of full plate / etc. just because of a little thing like physics.

[Kotenku]

Nominating this thread for Thread of the Year.

Really looks like ExileStrife enjoyed it.

[ThatsMathematics]

@ExileStrife:
Noooo! You clearly misunderstand. The entire basis of the Faraday Cage is that the cage is a conductor. If there is a field in the conductor then the charges are able to move around to neutralize the field. In order to do so, by Gauss' law, the charges MUST distribute themselves around the outside of the metal casing. Thus both the internal surface AND the inside of the shell are utterly safe.

If that shell happens to be grounded, it makes no difference. If the electric field within the closed shell is zero then the electric field inside is also zero: it doesn't care about anything around the shell. The external electrical world doesn't exist under ideal circumstances.

Even if you happened to be made out of metal (a brilliant conductor), you STILL would not conduct electricity, even if you were in contact with the Faraday cage.

The shell also doesn't heat up: significant heating effects occur under situations where there is ionization. The subsequent deionization releases heat and photons. A conductor doesn't need to ionize to conduct electricity.

I would be completely comfortable walking out into a thunderstorm in a closed metal suit. Or a car constructed from a metal shell, in fact. Such a car actually happens to be the second most safe place to be in a lightning storm. People often seem to think that it's the rubber tires that make it that way, but it's not. Lightning travels a long distance, and the breaking voltage of rubber is similar to that of air. Travelling through maybe a third of a metre of tire rubber isn't going to make much of a difference. In fact it's the Faraday cage effect which protects the inner components of the car, its fuel and anyone inside. They'd probably feel a mild, brief tingle since the cage is not perfect, but nothing remotely painful.

@LTS
Lightning is already an incredibly erratic force. A single bolt lasting a tiny fraction of a second generally consists of about half a dozen leading strikes and potent corresponding return strikes which release massive light and sound. For this reason the effect of a Faraday Cage is not completely perfect under those circumstances, but the first hand experience of humankind has shown that the Faraday Cage (in conjunction with the Skin effect) is more than sufficient to protect whatever is inside.

I don't know how much more erratic and powerful you want forgotten realms lightning bolt to get!

[ExileStrife]

If you were completely separated from the suit/faraday cage, I'd be agreeing with you.  The be-safe-inside-a-car example works along the same lines as my line-a-suit-of-fullplate-with-layers-of-low-conductivity-leather.  There's no argument there.

But yes!  The cage -is- a conductor.  And if you give that cage a hug, you become the conductor too!  Hook a lead of a car battery up to a giant bird cage, string a wire from the cage to a lightbulb, and put the other lead of the battery onto the other lead of the lightbulb.  The light comes on.  Current is flowing through the circuit, which includes the giant bird cage.  You can fly all you'd like around inside that birdcage without a care in the world because you'll be flying a constant electric field of 0.

But if you grab onto that birdcage, there's no arguing -- you become part of the circuit.  With just a car battery as the voltage source, you probably won't even notice it because your own resistance is magnitutes higher than the cage's, but current is indeed traveling through you.  All you need to do to raise that current is swap out the battery for a higher source, like a 10 MV transformer or a lightning bolt or something.

As far as the heating thing goes, we're talking about shitty metals used to make armors, not silicon that's been formed into a super-conducting lattice.  And even in super-conducting situations, if you want to move an electron, you can't do it without increasing entropy, and that's mostly likely going to come in the form of lost heat.

[Thomas_Not_very_wise]

Wow...this is an awesome thread.

Thread of the Year, IMO.

[Egon the Monkey]

Since faraday suits can be made of a wire mesh, surely any metal armor that's a full covering, including light chains should work? Anyway...

Reflex save spells (like lightning ones) are meant to be nasty to full plate wearers with low DEX and low reflex saves. A free defence against electrical would shift things in favour of heavy armor slightly, without a need. It's like saying wearing Fullplate should apply a -5/10% speed penalty all the time because it's heavy. Slightly unbalancing, and there's no real issue with it how it is. You can even get heavy armor with 5% electrical immunity if you like. Applying it to all, well how do you reckon that should be balanced out? Speed penalty? Vulnerability to heat from the thermal conductivity?

[Porkolt]

NWN =/= Real Life.
 
It obeys gravity and that's about the extent of it.

Oh yeah? What about hovering ravens?

[ThatsMathematics]

If you were completely separated from the suit/faraday cage, I'd be agreeing with you.  The be-safe-inside-a-car example works along the same lines as my line-a-suit-of-fullplate-with-layers-of-low-conductivity-leather.  There's no argument there.

Great.

But yes!  The cage -is- a conductor.  And if you give that cage a hug, you become the conductor too!  Hook a lead of a car battery up to a giant bird cage, string a wire from the cage to a lightbulb, and put the other lead of the battery onto the other lead of the lightbulb.  The light comes on.  Current is flowing through the circuit, which includes the giant bird cage.  You can fly all you'd like around inside that birdcage without a care in the world because you'll be flying a constant electric field of 0.

Here is where I begin to disagree with you. If you had a giant bird cage and exposed the cage to a large electric field, a bird flying through the cage would experience a decent proportion of the full electrical field strength. Why? Because a bird cage is mostly space along its outer surface. It's not even close to a closed conductor surface! The argument of the nullification of the cage's internal electric field cannot hold in a situation where a CLOSED Gauss surface cannot be entirely encased inside the thickness of the metal shell. Near complete nullification of the internal electric field occurs when a metal shell approximates a gauss surface (i.e. a shell with some relatively small openings, or a thick gauze).

But if you grab onto that birdcage, there's no arguing -- you become part of the circuit.  With just a car battery as the voltage source, you probably won't even notice it because your own resistance is magnitutes higher than the cage's, but current is indeed traveling through you.  All you need to do to raise that current is swap out the battery for a higher source, like a 10 MV transformer or a lightning bolt or something

It seems that I didn't explain this well enough. Suppose that you have a solid conducting mass in space (not hollow this time!). As it is a conductor, the charges in the mass redistribute such that the electric potential within the conductor is uniform and thus the electric field is zero.

It follows directly from Gauss' law that the charge concentrates solely at the surface of the mass. No other arrangement will permit an annulled electric field within the mass. Even if the inside of the mass is solid and conducting, there will be no movement of charge on the inside of the solid regardless. It experiences no current.

Now, suppose that your solid is a sphere of radius R. Take r < R, where we have a second sphere inside the first of radius r. This second sphere will be hollowed out and replaced with squishy, conductive human flesh. If this sphere were exposed to an electric field, there would still not be any current through the flesh. Put whatever you like on the inside which doesn't generate its own current. It just won't happen.

Similarly, take a conducting wire, or a conducting plane and connect it between ANY two inner surfaces of the cage. There will be no current.

On the other hand, if you were to touch the outside of that sphere then you would be exposed to the effects of the electric field. And if that field is powerful enough, then it will hurt.

There are more forces at work here than Ohm's law! Ohm's law is excellent at determining the properties of resistances in circuits, but it fails at explaining many of the phenomena of conductors in electric fields. It is an amazingly simple utility if I want to figure out how much heat and light will be dissipated by a tungsten filament in a lightbulb, bit it isn't nearly complex enough to explain why a Faraday cage works.

As far as the heating thing goes, we're talking about shitty metals used to make armors, not silicon that's been formed into a super-conducting lattice.  And even in super-conducting situations, if you want to move an electron, you can't do it without increasing entropy, and that's mostly likely going to come in the form of lost heat.

This is something that should really be left to the mathematics. I don't have the figure for the permittivity of non-stainless steel, but if it is a half-decent conductor then intuitively I don't imagine that the temperature produced would be nearly enough to breach the pain threshold. It's an interesting point, but as I say: we can't really make judgments either way until a mathematical simulation is conducted.

Of course, the severity of the effect will be affected by whether the player is going commando underneath his fullplate.

[DeputyCool]

A Wizard did it.