Electric potential inside an insulating sphere

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Discussion Overview

The discussion revolves around the calculation of electric potential inside an insulating sphere, specifically focusing on the choice of reference points for integration when determining potential from electric fields. Participants explore the implications of different reference points and the conceptual understanding of potential in relation to electric fields.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the electric field is integrated from infinity to a point inside the sphere, rather than from 0 to that point, highlighting confusion over the choice of reference point.
  • Another participant clarifies that the integration should always start from the chosen reference point, which can be arbitrary.
  • It is noted that setting the reference point at infinity is convenient because the electric field of a charge approaches zero at infinity, making it a natural choice for zero potential.
  • A participant proposes an alternative integration approach from r=0 to r=R and questions the conceptual difference in the resulting value.
  • Another participant agrees that integrating from r=0 to r=R is possible but notes that the result would differ by a constant, indicating a different reference point.
  • Concerns are raised about potential issues at r=0, suggesting that the nature of the charge distribution may affect the calculations.
  • One participant confirms that integrating from infinity is more convenient due to the potential being zero at that reference point.

Areas of Agreement / Disagreement

Participants express differing views on the implications of choosing different reference points for integration. While some agree on the convenience of using infinity, others raise concerns about the validity of integrating from r=0, indicating that the discussion remains unresolved regarding the best approach.

Contextual Notes

There are limitations regarding the assumptions made about the charge distribution (point charge vs. sphere of charge) and the implications of choosing different reference points for potential calculations. The discussion does not resolve these issues.

UMath1
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In the example my textbook has, the electric potential is calculating by integrating the electric field from infinity to R, radius of sphere, and then integrating the electric field from R to r, radius of point inside sphere. What I don't understand is why is the field integrated from infinity to r, why not 0 to r? How do you decide on the reference point? In an uniform electric field, the potential is calculated by integrating from to 0 to r.
 
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The integration is alwaysstarting from your reference (0 potential) location.
 
All kinds of potential have an arbitrary zero point, which is essentially a constant of integration. Infinity is just a handy choice of a zero point. Since the field of a charge drops off to 0 at infinity, setting a reference point at infinity is like setting a 0 potential reference point where there is no charge at all.
 
What about if you integrated the field from r=0 to r=R, radius of sphere? Why would that ot give you the right answer? Conceptually what is the difference in value?
 
You could certainly do that. The result would differ by a constant from the usual formula, which is fine. It would simply mean that you are taking the center as your reference instead of infinity.
 
You might find a small problem at r=0.
 
So it's just that integrating from infinity is more convenient as the voltage at infinity would be zero, correct?
 
Yup
 
Khashishi said:
You might find a small problem at r=0.
I think that he is considering a sphere of charge, not a point charge. So there shouldn't be a problem at r=0.
 

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