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Gauss' Law for finding E between metal plates 
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#1
Sep1111, 12:36 PM

P: 68

I'm having some difficulty applying Gauss's Law to metal plates. From what I've studied it seems to me that Gauss's Law only really works when there is spherical symmetry, in all other cases it is an approximation. Am I correct in inferring this?
However, in a case where the distance between two charged metal plates is small compared to their length, Gauss's Law can be applied to find electric field between the plates by the equation E = [itex]q/[/itex][itex]\epsilon[/itex]A My question is what if the distance between the plates is now increased, according to Gauss' Law the electric field would be the same. But according to Coulomb it should go down, so what really happens in this case? 


#2
Sep1111, 01:51 PM

PF Gold
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#3
Sep1211, 08:22 AM

P: 68

I'm just curious about the physics of the flux law. I know Gauss' Law requires an infinitely long plane placed very close to the metal plate to work. And there are problems with fringing so it is only effective to consider the field near the centre of the plate.
My first question was a theoretical one: whether the Law works perfectly only in cases of spherical symmetry, and is only useful as an approximation in other symmetries. As for the separation between the plates increasing slightly, my understanding is that practically if I'm using Gauss' Law the field increase is minimal since the length of the plates is much much greater than the separation. So I can claim that the field remains the same by continuing to use the formula I mentioned, if I'm not doing the surface integral. Is this correct in terms of the physics of it? 


#4
Sep1211, 12:55 PM

PF Gold
P: 3,080

Gauss' Law for finding E between metal plates



#5
Sep1211, 02:46 PM

P: 68

Okay that takes care of my doubts. Just one further thing, I was trying to find out how Gauss invented the flux law but couldn't find anything useful. Did he find it independently of Coulomb's Law? Just curious about the formulation of his law, I can't imagine what would make him relate the effect of charges and fields to the area of an enclosing surface.



#6
Sep1211, 03:17 PM

HW Helper
P: 3,446

Coulomb's law came waay before Gauss' law.
Gauss' law (in differential form) is one of the 4 Maxwell equations. And since Maxwell's equations are the most fundamental laws of classical electrodynamics, I would say Gauss' Law is more fundamental than Coulomb's law. In fact, you can prove Coulomb's law If you assume Gauss' law is true. EDIT: actually, I think you can also prove Gauss' law by assuming Coulomb's law. I think the two laws are equivalent, so I guess they are just as fundamental as each other. The reason I prefer Gauss' law (in differential form) is because it looks simpler than coulomb's law. 


#7
Sep1211, 08:23 PM

P: 68

So did he find out the general divergence theorem and then apply it to electric fields? From math to physics, then?



#8
Sep1311, 06:54 AM

HW Helper
P: 3,446

According to wikipedia, yes he already knew about the general divergence theorem before he came up with his law for the electric field.
I also read on wikipedia  Coulomb's law is only true for stationary charges, but Gauss' law is true even for moving charges. So Gauss' law is more fundamental. 


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