Understanding the Equation ε=ΔV/r: Parallel Plates vs. Point Charges

Click For Summary

Discussion Overview

The discussion revolves around the equation ε=ΔV/r and its applicability to different configurations, specifically comparing parallel plates to point charges. Participants explore the implications of this equation in the context of electrostatics, including the use of calculus in deriving electric field values.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the equation ε=ΔV/r is valid only for two parallel plates or if it can also be applied to point charges.
  • Another participant provides a link to a Wikipedia article discussing electric potential due to a point charge, suggesting a reference for further exploration.
  • A participant expresses enthusiasm for the topic of electrostatics, indicating a personal interest in the subject matter.
  • One participant points out that the equation may be an approximation and relates it to the expression |E| = ΔV/Δr, emphasizing that a more accurate value is obtained by taking the limit as Δ approaches 0, leading to E=-∇V. They note that while the two approaches yield the same result for infinite parallel plates, a curved electric field requires a smaller step size for accuracy.

Areas of Agreement / Disagreement

There is no consensus on the applicability of the equation ε=ΔV/r to point charges versus parallel plates, and participants express differing views on the accuracy of the equation in various contexts.

Contextual Notes

Participants highlight the importance of considering the configuration of the electric field and the limitations of approximations when applying the equation. The discussion includes unresolved mathematical considerations regarding the transition from finite to infinitesimal changes.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of electrostatics, particularly those interested in the mathematical foundations and applications of electric field equations in different scenarios.

BlueCardBird
Messages
25
Reaction score
0
For the equation ε=ΔV/r, does this work only between 2 parallel plates or would it work for point charges as well?
 
Physics news on Phys.org
I love Electrostatics <3
 
Do you know calculus? Your equation seems to be another way of writing |E| = \Delta V/\Delta r, which is only an approximation. The correct value is gotten by taking the limit as Delta goes to 0. Then you get:
E=-\nabla V
In the special case of infinite parallel plate, they give the same answer, but for a curved E field you get a more accurate answer for smaller step size.
 

Similar threads

High School Curious about the uniform electric field between metal plates
  • · Replies 8 ·
Replies
8
Views
2K
High School Electric Field Created by 2 Infinite Plates
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Electric Potential in circuit
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Parallel plate capacitor, charge imbalance VS charge redistribution
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Magnetic field when the area of the plates of a capacitor increases
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Magnetic field inside a capacitor
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Electric field outside a parallel plate capacitor
  • · Replies 7 ·
Replies
7
Views
20K
Undergrad Electric Field of Uniformly Charged Infinite Plane
  • · Replies 6 ·
Replies
6
Views
478
High School Electric Field Created by a Finite Plate
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Speed of Electricity in Plate Capacitor & Cable
  • · Replies 18 ·
Replies
18
Views
2K