Uniqueness/Gauss Theorem - General Difficulty/Misconceptions?

[rbrayana123]

I'm hoping this is an appropriate question for this forum since its related to coursework. If not, sorry in advance!

I've been going through Purcell and managed to get through the first two chapters (with unanswered questions here and there but still looking!) but with Chapter 3 (Conductors & Capacitors), I've hit a dead end when it comes to solving ANY problem.

I've tried watching various YouTube videos and different resources but it seems like I just end up being familiar with specific examples and cases rather then how to apply the Uniqueness Theorem (or even Gauss).

For example, this video right here has an example: http://www.youtube.com/watch?v=gKf2szoEEBE&t=13m34s

My questions are:

1) What new knowledge does equating the two conductors to having no charge offer? After some head scratching, I can see why that's the only other case, outside of the infinite possibilities of distributing charge on the surface and the varying magnitudes of the charge.

2) What exactly are the boundary conditions? My rudimentary understanding is that the potential is constant for the surface and(/or?) charge in a conductor can be distributed in any manner.

3) I'm also having specific trouble applying Gauss' Theorem and Uniqueness Theorem together. I've read somewhere a cavity within a conductor has an electric field of zero but when I try to think about concentric spherical shells, I'm not sure if it holds true.

4) Also, is Gauss' Theorem only applicable for some sort of infinite entity? For example, a finite line charge SHOULD have an electric field in the direction of its extension so there is a flux but with infinite fields, the argument is they cancel out at the ends? Or is this correct.

 

[rude man]

4) Also, is Gauss' Theorem only applicable for some sort of infinite entity? For example, a finite line charge SHOULD have an electric field in the direction of its extension so there is a flux but with infinite fields, the argument is they cancel out at the ends? Or is this correct.

I will address only this item for the moment:

If you wrap a finite Gaussian surface (a right circular cylinder) around an infinite wire, the E field is strictly radial thruout the length of your cylinder, making it easy to calculate the field at any radius inside or outside the wire.

If the wire had finite length the E field would not be only radial. There would be a component of E thru the cylinder's end faces. The cylinder ends would thus have a finite E flux going into them, invalidating the idea that ∫E*dA = q/ε = 2πrLE where q is the total charge, and L the wire's length, within the cylinder.

 

[rbrayana123]

Hello! Just wanted to say I've better grasped questions 1 & 3 and thank you for graciously replying to question 4! I'll still be trying to answer my 2nd question and will later post in this thread on my progress.

I feel slightly annoying asking so many questions on this forum. However, I guarantee it's only because I'm simply not in a university environment over winter break so it's a little difficult having meaningful conversations about these topics alone. Again, thanks!