Electrostatics- Charged Identical Spheres

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Discussion Overview

The discussion centers around the electrostatics of identical charged spheres, specifically why two identical spheres that are briefly touched or connected by a conducting wire should share an equal charge after separation. The conversation explores concepts related to charge distribution, electric fields, and electric potential, with participants expressing varying levels of understanding and familiarity with the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant questions why identical spheres should have an equal charge after being touched, particularly when one is initially charged and the other is neutral.
  • Another participant suggests that if the spheres were not identical, the resulting electric field would induce a current that equalizes the charges quickly, assuming the spheres are reasonably conductive.
  • A participant expresses confusion about the explanation provided and requests further elaboration on the concepts discussed.
  • One participant mentions that the topic is new to them and notes that their textbook does not explain why identical spheres share charge equally, indicating a lack of knowledge about electric fields.
  • Another participant discusses the importance of calculations in electrostatics, mentioning the need to prove that charge resides on the surface of conductors and referencing electric potential integration.
  • A participant explains that when two spheres are touched, they act as one conductor, leading to an even distribution of charge due to their identical surface areas and symmetry.
  • Further clarification is requested on the role of electric potential in pushing charges to the surface of conductors and on the integration process mentioned in the context of electric potential.
  • One participant acknowledges their limited understanding of electric potential, only being familiar with the formula kq/r.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and familiarity with the concepts discussed. There is no consensus on the explanations provided, and multiple viewpoints and levels of comprehension are present throughout the discussion.

Contextual Notes

Some participants indicate a lack of foundational knowledge in electric fields and electric potential, which may limit their understanding of the topic. There are references to mathematical integration and electric potential that remain unresolved in the discussion.

Who May Find This Useful

Students beginning their studies in electrostatics, individuals interested in the principles of charge distribution, and those seeking clarification on the behavior of conductors in electrostatic scenarios may find this discussion relevant.

Isaac Sanctis
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In electrostatics, why is it that identical spheres that are touched for a brief moment or connected by a conducting wire (wire not gaining any charge) should have an equal charge? Why is that they come in an equilibrium of charge?
For example - If we take 2 identical spheres one bearing a charge q and the other neutral. The spheres are touched for a brief moment after which they are separated. Then it is stated that they both bear a charge of q/2 because they are identical ? But why so ?
 
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If they were not, the resulting electric field would induce a current which equalises the charges. If the spheres are reasonably conductive, this process happens very fast.
 
Could you please elaborate?
 
Which part do you have problems understanding?
 
All what you said... This topic has just been started with me in my classes and as I went through the Fundamentals of Physics (6th edition) Electric Charge, it's not stated why two identical spheres should have a equally shared net charge. And I have no knowledge of electric fields whatsoever.
 
Isaac Sanctis said:
All what you said... This topic has just been started with me in my classes and as I went through the Fundamentals of Physics (6th edition) Electric Charge, it's not stated why two identical spheres should have a equally shared net charge. And I have no knowledge of electric fields whatsoever.
this requires calculation. EM has many integration. First, you have to prove that there is no charge not on the surface of a conductor. I think this is proved by integrating electric potential of a sphere. When electric potential is minimum along an axis, it is maximum on another axis (not sure about sphere, I only calculated the ring). This solution is very important. It explains why charges in conductor must be on surface.

So, back to your question, I think you can think like this, the electric potential will push the charges on to the surface of the conductor. As you touch two spheres together, they are combined together, become one conductor, all charges go on surface evenly, when you separate them, charges on each sphere is q/2, reason is the surface area of two spheres are the same, also sphere is perfectly symmetric, that makes charges evenly distributed when two spheres are in contact.

hope you understand, you can simply integrate electric potential of a point lying on an axis, then use find out the maxima. then do this integration again for a point on another axis, then find out maxima again. For both cases, they should give different formula, and there should be at least one of the two solutions is not minimum.
 
sunmaggot said:
This solution is very important. It explains why charges in conductor must be on surface.
Can you elaborate on this point please ?
Thank you sunmaggot.
Apart from that I did understand everything except the below
"I think you can think like this, the electric potential will push the charges on to the surface of the conductor."

and

"hope you understand, you can simply integrate electric potential of a point lying on an axis, then use find out the maxima. then do this integration again for a point on another axis, then find out maxima again. For both cases, they should give different formula, and there should be at least one of the two solutions is not minimum."

Also I have no idea on electric potential but just given a formula i.e. kq/r
 

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