Deriving the Equation for Area of a Ring

  • Context: Undergrad 
  • Thread starter Thread starter Calpalned
  • Start date Start date
  • Tags Tags
    Area Ring
Click For Summary

Discussion Overview

The discussion revolves around the derivation of the equation for the area of a ring, exploring different approaches and interpretations related to the mathematical formulation. The scope includes mathematical reasoning and conceptual clarification.

Discussion Character

  • Mathematical reasoning, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant proposes deriving the area of a ring as the difference between the areas of two circles, expressed as ##\pi(R+dR)^2 - \pi R^2##.
  • Another participant questions the equivalence of the derived expression ##\pi(R+dR)^2 - \pi R^2## to the given approximation ##(2/\pi R)(dR)##, indicating uncertainty about this relationship.
  • A later reply clarifies that the expression is an approximation valid for small values of ##dR##.
  • Another participant notes that when setting up integrals, the differential is considered to be vanishingly small, allowing for the neglect of higher-order terms involving the differential.

Areas of Agreement / Disagreement

Participants express differing views on the equivalence of the derived area expression and the given approximation, indicating that the discussion remains unresolved regarding this relationship.

Contextual Notes

The discussion highlights assumptions about the size of the differential ##dR## and the treatment of higher-order terms in the context of integration, which may affect the validity of the approximations used.

Calpalned
Messages
297
Reaction score
6
How was the equation for area of a ring derived?
 

Attachments

  • Screenshot (55).png
    Screenshot (55).png
    24.5 KB · Views: 441
Physics news on Phys.org
I can derive the area as the difference of the areas of two circles. ##= \pi(R+dR)^2 - \pi R^2##
But I don't think this ##\pi (R+dR)^2 - \pi R^2## is equal to ## (2/pi R)(dR)## given in the beginning.
 
Calpalned said:
I can derive the area as the difference of the areas of two circles. ##= \pi(R+dR)^2 - \pi R^2##
But I don't think this ##\pi (R+dR)^2 - \pi R^2## is equal to ## (2/pi R)(dR)## given in the beginning.

No, but it's an approximation for small ##dR##.
 
When setting up integrals, the differential is assumed to be vanishing small, so that terms proportional to the powers of the differential can be neglected.
 

Similar threads

Finding Area of Ring Segment to Find Electric Field of Disk
  • · Replies 10 ·
Replies
10
Views
2K
How to find motional emf w/o an equation for mag field?
  • · Replies 7 ·
Replies
7
Views
855
Can a belly button ring travel through a person like a bullet?
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Electric field of ring at any point
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How to do resistance (spot) welds by using arc/TIG welder?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Bead on a vertical frictionless ring
  • · Replies 20 ·
Replies
20
Views
2K
Potential difference of a ring rolling in magnetic field
  • · Replies 34 ·
2
Replies
34
Views
4K
Direction of current as bar magnet moves uniformly through copper ring
  • · Replies 3 ·
Replies
3
Views
1K
High School The ONE Ring has been Found
  • · Replies 2 ·
Replies
2
Views
1K
Number of Decks on a Rotating Habitat
  • · Replies 9 ·
Replies
9
Views
3K