Limits of integration for electric potential

Click For Summary

Discussion Overview

The discussion revolves around the limits of integration used in calculating electric potential, specifically in the context of integrating contributions from ring elements of a disk. Participants explore why the limits are set from 0 to R_0 rather than from 0 to x.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the choice of integration limits, suggesting that integrating from 0 to x is more typical when finding potential energy and electric fields.
  • Another participant explains that the potential at point P is calculated by summing contributions from different ring elements, which necessitates integrating from 0 to R_0.
  • A subsequent reply seeks clarification on whether integrating from 0 to x would be invalid in this context.
  • One participant confirms that integrating from 0 to x would not be appropriate, as the distance x to point P is treated as a constant in this scenario.
  • Another participant reiterates the point about the integration being a sum of contributions that do not vary with x.

Areas of Agreement / Disagreement

Participants generally agree on the reasoning behind the choice of integration limits, but there is a lack of consensus on the implications of integrating from 0 to x, as one participant questions its validity.

Contextual Notes

The discussion does not resolve the implications of integrating from 0 to x, leaving the validity of that approach open to interpretation.

Calpalned
Messages
297
Reaction score
6
In the example in the picture, we can see that they chose the limits of integration to be from 0 to R_0. Why didn't they choose x (that is, from 0 to x)? Isn't that what we normally integrate over when we find potential energy and electric fields?
Thank you
Screenshot (55).png
 
Physics news on Phys.org
Here we are adding potential at P due to different ring elements. The disk is considered as large numbers of thin rings with radii varying from 0 to R0 hence the potential due to a ring element is integrated for radius 0 to R0.
 
That makes sense... so integrating from 0 to x would be invalid?
 
Yes, actually integration is the sum and we are here adding nothing which is varying with x. The distance x of P is a constant.
 
mukundpa said:
Yes, actually integration is the sum and we are here adding nothing which is varying with x. The distance x of P is a constant.
Ok thank you. I understand now
 
welcome.
 
  • Like
Likes   Reactions: Calpalned

Similar threads

  • · Replies 21 ·
Replies
21
Views
4K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K