Charge Redistribution in Conducting Objects

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Discussion Overview

The discussion revolves around the concept of charge redistribution in conducting objects when they come into contact. Participants explore the implications of charge distribution, particularly when one object has a small number of excess electrons while the other is neutral. The scope includes theoretical considerations and conceptual clarifications regarding electrostatics and charge behavior in conductors.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that when two conducting objects touch, charges will distribute equally, but question how this applies when one object has only three excess electrons and the other is neutral.
  • One participant suggests that two touching conductors can be treated as a single object, implying a unified charge distribution.
  • Another participant explains that the equal distribution model applies when the number of electrons is large enough to treat charge density as continuous, using an analogy of a beach's surface to illustrate this point.
  • It is noted that the model of equal distribution does not hold for a small number of electrons, as they will arrange themselves to minimize potential energy, and the exact shapes of the objects would be necessary for precise calculations.
  • One participant emphasizes that the assumption of equal distribution relies on having a large number of charges, and questions the validity of this assumption when dealing with only three excess electrons.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the equal charge distribution model in scenarios involving a small number of excess electrons. There is no consensus on how charge redistribution occurs in such cases, indicating ongoing debate and uncertainty.

Contextual Notes

Limitations include the assumption that charge distribution can be treated as continuous, which may not hold for small numbers of charges. The discussion also highlights the dependence on the shapes of the conducting objects for accurate calculations of charge arrangement.

Samanko
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I know that if two conducting objects touch each other, the charges will distribute equally over the objects.
What if one object has 3 excess electrons, one is neutral?
How can the charge distribute equally over two objects?
 
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Two touching conductors act like a single object.
 
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That bit about how "the charges will distribute equally over the objects" applies when the number of electrons is large enough that we can treat the charge density as a continuous function instead of thinking about individual electrons. It's somewhat analogous to the way that I can talk about the smooth surface of a beach sloping evenly towards the water, even though we know that at a sufficiently small scale the beach is made up individual grains of sand - we don't know where each grain of sand is, but we know that together they arrange themselves to form a beach that we can describe as a continuous smooth surface.

Of course this approach won't work if we have just three grains of sand, and the "distribute equally" model doesn't work for three electrons either. The electrons will arrange themselves in a way that minimizes the potential energy; we'd need to know the exact shapes of the two objects to calculate what that arrangement will be.
(If you have a very large number of electrons, then doing that calculation will yield the same result as "distribute evenly"; the latter is much easier to calculate with, so that's what we use whenever it is applicable).
 
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Samanko said:
I know that if two conducting objects touch each other, the charges will distribute equally over the objects.

That's true if the objects have the same size and shape. What's the same is the electric potential.

What if one object has 3 excess electrons, one is neutral?
How can the charge distribute equally over two objects?

It can't! The formulas assume that there are a very large number of charges. This condition is satisfied even if you have a differential element of charge ##dq##! It's macroscopically small yet microscopically large.
 

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