Charge distribution on an irregular conducting surface

Click For Summary

Discussion Overview

The discussion revolves around the charge distribution on an irregular conducting surface, specifically addressing how charge density varies with the curvature of the surface. Participants explore theoretical explanations and analogies involving spheres of different sizes and their implications for charge density and electric potential.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that charge density is less on surfaces with greater radius of curvature, suggesting a relationship between curvature and charge distribution.
  • Others argue that this is not universally true and present a counterexample involving two spheres of different sizes at the same potential, where the smaller sphere exhibits a stronger electric field and thus a larger charge density.
  • A participant questions the applicability of the sphere analogy to irregular bodies, prompting further clarification on how curvature affects charge density.
  • It is suggested that the geometry of the surface, particularly in notches, influences charge density, with low charge density being attributed to the specific geometry rather than the surface area.
  • Another participant challenges the idea that surface area relates to charge density, asserting that the electric field strength is the key factor affecting surface charge density.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between curvature, charge density, and electric potential. There is no consensus on the validity of the initial claim regarding charge density and curvature, and the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the importance of geometry and electric field strength in understanding charge distribution, but the discussion contains unresolved assumptions regarding the relationship between potential and charge density.

Aman Chauhan
Messages
6
Reaction score
0
I recently read that the charge density is less on surfaces with greater radius of curvature on the surface of a charged irregular conducting body . if anyone can provide a proof or explanation , please help!
 
Physics news on Phys.org
That is not always true, but often it is a good approximation.
Consider two spheres of different size far away from each other at the same potential. If you calculate their electric field strengths at the surface, you will see that the smaller sphere has the stronger field, which corresponds to a larger charge density.
 
mfb said:
That is not always true, but often it is a good approximation.
Consider two spheres of different size far away from each other at the same potential. If you calculate their electric field strengths at then surface, you will see that the smaller sphere has the stronger field, which corresponds to a larger charge density.
Agreed! Because when there is same potential on both smaller and larger spheres, the charged atoms on smaller sphere will be very near where as due to more area of larger sphere, there is not space between charges atoms. Here both the potential difference and radius of curvature in case of spheres matters. :)
 
I am able to understand your explanation . But how can you say that this situation of 2 different sized spheres is equivalent to an irregular body which is just more curved at some points.
 
Every part of the surface is at the same potential. If the more curved parts are exposed, the situation is similar to the small sphere. If they are hidden somewhere in a notch, their charge density can be small.
 
Sorry I could not understand what you meant by "hidden somewhere in a notch". please elaborate a bit.
 
Like this:

charge.png
 
Is this low charge density at the notch due to great repulsion from nearby charges (i suppose) Or is there some other reason ?
 
It is low due to the specific geometry here.

The electric potential is roughly the same everywhere in the notch (it is exactly the same everywhere at the surface!), which leads to low charge concentrations at the surface.
 
  • #10
OK, So since the potential at every surface has to be the same and there is more surface nearer to a point in the notch so the charge density has to be less there in order to make the potential same as that of every point. Is that what you meant? (a rough approx. I mean)
 
  • #11
The surface area has nothing to do with that, and there is no meaningful relation between potential (as absolute value) and charge density here.
The electric field is weaker, and surface charge density is proportional to the field at the surface.
 

Similar threads

Graduate Infinite scaling limit of an elliptic charged surface
  • · Replies 5 ·
Replies
5
Views
421
Undergrad Help with FLP argument of non-uniformly distributed surface charges
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Gauss' law and an object with nonuniform charge distribution
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Charging a small metal ball from a charged hollow sphere
  • · Replies 4 ·
Replies
4
Views
2K
High School Definition of ground potential in infinite sheet charge distributions
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Work done by electric field of an irregularly shaped conductor
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Surface charge density of a conducting spherical shell
  • · Replies 3 ·
Replies
3
Views
7K
Undergrad Surface charge of neutral solids
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Confusion over applying the 1st uniqueness theorem to charged regions
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Electric Field inside the material of a hollow conducting sphere
  • · Replies 11 ·
Replies
11
Views
4K