Gauss' Law and the Faraday Cage

[ThatsMathematics]

First of all, I want to begin by stating how awesome the EFUA DMs and players are!

As the title of my post probably makes it clear to most of you that I am about to bring Science to the DnD game table, I'm sure that a lot of you are already rolling your eyes in exasperation by now. I nonetheless beg that you bear with me, as the science which follows bears a lot of pertinence to a setting such as ours in which flying bolts of lightning are a common hazard.

THE FARADAY CAGE! It is the effect of electromagnetic shielding which occurs when a conducting material (e.g. iron and its alloys) forms a closed surface. The short explanation is that the inside is shielded against the effects of static electric fields.

For the more curious:
----WARNING! TECHNICAL EXPLANATION----
We define infinitesimal electrostatic flux as follows:
dF = E.dS
Where E is the electric field function, and dS is an infinitesimal surface vector. In closed surfaces, it is directed towards the outside of the surface.
Gauss' Law states that if such a surface is closed then the flux is defined by a quantity which is dependent solely on contained charges:
F = (integral over the closed surface)E.dS = (interior chage)/(electric constant)

Now take any closed surface that you please. Up to a length of l on each side of this surface will be a conducting shell, such that the shell is itself closed but (with l sufficiently small) still hollow. Since the shell is a conductor, charges inside the conductor will reorient themselves such that the net electric field within the material of the conducting shell is zero.

Take the Gauss surface, which by the definition of our conducting shell, contains half of the width of the conducting shell. At the surface, the electric field E = 0. We have:
F = (integral over the closed surface) 0 . dS = 0 = (interior charge)/(electric constant)
(interior charge) = 0
This means that the electric field is not just zero in the material of the conducting shell but also in the hollow space within the shell. We conclude that the inside of this conducting shell, which we call a Faraday cage, is shielded from the electric influences of the outside world.
----END OF TECHNICAL EXPLANATION----

This effect applies to near-closed conducting surfaces too. Do you see where I'm going with this?

Plate mail would make a bloody awesome Faraday cage, especially if accompanied with a metal helmet! Why is a player wrapped thoroughly in a shell of highly conductive material equally susceptible to lightning and electric shocks as a man wrapped in cloth?

I propose that, in accordance with good sense and Gauss' law, any creature wearing plate mail receive at least a high partial lightning immunity effect which may or may not be further increased by the wearing of a helmet. Lighter forms of heavy armor might have a lesser protective effect.

Whilst I do not presume to know anything about NWN scripting, I imagine that implementation could occur equally at the level of spell scripts (i.e. explicitly adding the feature to the individual lightning spells to reduce or eliminate damage depending on the armor worn), or at the level of the OnEquip scripts which adds a temporary electrical immunity effect to plate mail when equipped. This will eliminate tedious mass-replacement of platemail and prevent the cost of platemail from rising in scripted stores which comes from an implementation brought about by directly editing the properties of plate mail. I imagine that both implementations would be fairly simple.

[Semli]

[Paha]

The thing is also, this is not a world where laws of physics or so live on normally. Gods, magic and the whole lot is reality in this game world.

And using that as my argument, when I throw a bolt of lightning at you, you will be fried with armor as much as without armor, unless you have somekind protection from such elements, that meaning a different material or magical protection.

If we'd use this kind of laws and set up a partial protection from such to normal items, then we would start to set tricks for other elements and aspects of the world to counter that part or apply weaknesses to others. It'd be endless loop which we can't get out of.

[ThatsMathematics]

You say that science has no place in the Forgotten realms, but is that really the case? Science is assumed as the default convention when no setting details are explicitly given to oppose those laws (e.g. magic).

For instance:

• When a player climbs a mountain, the player is assumed to have done a lot of work in doing so and will have exhausted himself.
• If that player then falls off of that mountain (e.g. if he is pushed), then the potential energy gained in the climb will contribute to the kinetic energy of the fall. The player probably won't survive the impact of the ground due to the inelasticity of the collision.
• Wheels are still the most effective means of circumventing forces of static friction when pulling carts.
• Again with static friction, sheer, high walls can't just be scaled by players due to an inability of those forces to overcome the force of gravity.
• The sun rises in the morning and descends again at night
• The universe has compasses which (we assume) are operated via the effects of magnetic fields
• Dead bodies rot and decompose and smell an awful lot. That's the science of phagocytes.
• The traits of a child are a recombination of some of the traits of the father, and some of the traits of the mother. We observe this in orc-human or orc-demon pairings for example. (i.e. genetics)
• Whist the mechanism is not directly observed in the EFUA game world, people in the setting must replenish their dwindling supplies of chemical energy with nourishment, and so there seems to be conservation of energy where magic is not involved.

So why not Gauss' law too? Forgotten realms lightning seems mostly consistent with our own lightning anyway.

[Semli]

[Letsplayforfun]

If you pray Talos hard enough, you change the variables.

[Finktank]

If you want to play a scientist and use science, go play a World of Darkness or Eberron game. Failing that, try Alternity.

This is a fantasy game with gods and magic.

[chrijone]

Science has room in Dnd Gnomes!

[Fliggin McButton]

Be nice Fink. The man makes a good point, and he is correct, however I can firmly state that while your science is spot on and it can't really be logically refuted, its not gonna happen.

Why? Well, it gives an advantage to plate wearers that other characters wouldn't have, and plate wearers get some advantages anywho.

Your a smart man, and your suggestion is valid in a realistic sense, however balance must be maintained.

[lovethesuit]

I know of another Faraday. Crazy little guy with a penchant for time travel. BUT I'M GUESSING YOU WOULDN'T KNOW ANYTHING ABOUT THAT WOULD YOU DANIEL!

Anyhow I wouldn't say plate mail is enclosed or a shell it's layered pieces of metal often over leather and cloth and I would also say that most electricity-based spells are rather erratic and unpredictable, more like lightning from the sky than say in a controlled lab environment. Under precise conditions with the right plate mail, sure, I could see this working. But I also think that considering the fact lightning spells, being magic, would usually be more powerful than the natural stuff, and the other conditions I've mentioned, it's unfeasible and undesirable to implement your immunity proposition at this time.

[lovethesuit]

Also the sun and moon are gods in this setting

Almost everything is a fucking god

so

[lovethesuit]

We should also consider that the "closed" whatever mentioned is not hollow, but inhabited by a sweaty fleshy human which as we all know makes a great conductor.

choo choo

all aboooard

the love train

[ExileStrife]

As you walk in your shiny faraday cage/suit, the suit is always grounded

Guess what happens when you touch a grounded faraday cage that has current traveling through it?  Current travels through you, too!  And that current is inversely proportional to your body's total resistance compared to the metal container's total resistance.  That's even if there's not a perfect grounded connection from you to somewhere else.  You become "part of the cage" if you are inside the cage and grab onto it.  Since your body's resistance is relatively high compared to a nice conducting metal's, it will certainly get a smaller share of the total current in the system, but when we're talking about magical lightning bolts and divine lightning storms, that's still enough to kill you.

[DeputyCool]

A good suggestion, really, but one we're unlikely to implement. Still, don't let some of the naysayers discourage you from posting, Mathmatics.


And welcome to EFU!

[Porkolt]

We should also consider that the "closed" whatever mentioned is not hollow, but inhabited by a sweaty fleshy human which as we all know makes a great conductor.
 
choo choo
 
all aboooard
 
the love train

You know the human body is actually a very bad conductor, right.
 
It varies between 1.000 and 100.000 Ohms, which is pretty bad compared to, for instance, steel (you know, that suit he's wearing), which has a resistance of 1 x 10^-7 Ohms.
 
So it's actually pretty likely that any form of electrical current applied to the armor will pass into the earth without going through the body first.