Electric field inside a hollow conductive sphere

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Discussion Overview

The discussion centers around the behavior of the electric field inside a hollow conductive sphere, particularly when a very small charge, such as two electrons, is placed on it. Participants explore theoretical implications, assumptions about charge distribution, and the nature of free electrons in metallic conductors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant, Tony, questions whether the electric field inside a conducting sphere remains zero when only a very small charge, like two electrons, is present, suggesting that the charge distribution may not be uniform.
  • Another participant argues that a conducting sphere contains a vast number of free electrons that can redistribute evenly, implying that the presence of two additional electrons would not affect the overall electric field inside.
  • A third participant supports this view by stating that the fundamental theorems about conductors assume a large number of conduction electrons, indicating that the addition of a small number of electrons does not significantly alter the electric field.
  • Tony further inquires about the nature of free electrons in metallic conductors, questioning whether they represent an excess of electrons compared to protons and how this relates to the overall charge of metals.
  • Another participant clarifies that while there are as many electrons as protons in a neutral metal, a fraction of the electrons are free to conduct electricity, distinguishing them from valence electrons that are bound to atoms.

Areas of Agreement / Disagreement

Participants express differing views on the implications of having a very small charge on a conductive sphere, with some asserting that the electric field remains zero due to the behavior of free electrons, while others question this assumption based on the specific conditions of the charge. The discussion remains unresolved regarding the impact of a minimal charge on the electric field.

Contextual Notes

The discussion highlights assumptions about charge distribution and the behavior of free electrons in conductors, which may depend on specific conditions and definitions that are not fully explored in the thread.

TonyZ
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Hello,
This is my first post to these forums.

It is well known that the electric field inside a conducting
sphere is zero everywhere inside. But what if the charge
placed on the sphere is very, very small. Let's say it
consists of only two electrons. Clearly, this small charge cannot
be evenly distributed on the surface of the sphere. The
two electrons will undoubtedly end up as far apart as possible,
i.e. at opposite sides of the sphere. It doesn't appear that
the electric field is zero everywhere inside this sphere.

I'd like to get the group's input on this.

Thanks!
Tony
 
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A conducting sphere will have many free electrons, and it will be no problem for them to spread evenly.
A charged sphere of copper might consist of 10^24 copper ions and 10^24+2 electrons in the conduction band that can all move around.
 
The theorems about conductors generally assume a huge number of conduction electrons as willem2 says. If only two electrons are added to a conductor, the lare number of conduction electrons will realign to produce zero field inside. That is, adding two newborns to the world population does not change much, except for their families.
 
Thanks to all who replied! I understand what you are saying.

I have one other question: Are the "free electrons" in a metalic conductor those which are above and beyond the ones that are part of the metal atoms? For example, copper atoms have 29 electrons and 29 protons. Does having free electrons mean there are more electrons than protons? If so, wouldn't that mean that every metal is inherently
negatively charged (which I know is not correct)?

Thanks,
Tony


Tony
 
TonyZ said:
I have one other question: Are the "free electrons" in a metalic conductor those which are above and beyond the ones that are part of the metal atoms? For example, copper atoms have 29 electrons and 29 protons. Does having free electrons mean there are more electrons than protons?

There are as many electrons as there are protons. A fraction of the 29 are conducting and the rest are not (valence electrons). I don't know how many of the 29 are valence and how many are conducting, but it should be a well-known constant number at room temperature for copper specialists (probably in a table somewhere, and quite readily calculable with the basic theory).

In condensed matter/solid state theory, a crystal (including a metallic polycrystal) is considered a lattice of (+) ions, through which conducting electrons flow, not a lattice of (neutral) atoms.
 

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