Induced charge density -- non-zero potential case

Click For Summary
SUMMARY

This discussion focuses on calculating induced charge density on the surfaces of non-grounded conductors using Poisson's equation, represented as ∇²U = -ρ/(εε₀). The conversation highlights the limitations of analytical solutions for arbitrary geometries and emphasizes the necessity of employing Finite Element Analysis (FEA) for complex shapes. Participants seek examples and solutions that illustrate the application of FEA in determining charge density distributions in non-zero potential scenarios.

PREREQUISITES
  • Understanding of Poisson's equation and its applications in electrostatics.
  • Familiarity with Finite Element Analysis (FEA) techniques.
  • Knowledge of electrostatic principles, particularly induced charge density.
  • Basic grasp of mathematical methods for solving differential equations.
NEXT STEPS
  • Research the application of Finite Element Analysis in electrostatics.
  • Study examples of solving Poisson's equation for non-standard geometries.
  • Explore software tools for FEA, such as ANSYS or COMSOL Multiphysics.
  • Investigate series expansion methods for charge density calculations in complex systems.
USEFUL FOR

Electrostatics researchers, electrical engineers, and students studying advanced electromagnetism who are interested in the practical applications of charge density calculations and Finite Element Analysis.

mertcan
Messages
343
Reaction score
6
Hi, Let's think 2 arbitrary shape conductors with non zero charged. If these 2 conductors are closed, there will be induced charge density over surfaces of these conductors. I have not seen such an example, instead there are lots of problems which involve zero(grounded) potential case and method of images theorem is applied. So, I am asking how can we mathematically find induced charge density over conductors' surfaces including non zero potential case(not grounded)?
Thanks...
 
Last edited by a moderator:
Physics news on Phys.org
Finding charge density distribution involves solving Poisson's equation ## \nabla ^2 U = - \frac {\rho}{\epsilon \epsilon_0} ##.
This equation can be solved analytically only in some simple cases when the geometry is rather regular (e.g. planar, cylindrical, spherical, etc.) and these you find in textbooks. In other cases, you can get a power (or other) series expansion. But if you want to solve the Poisson's equation for a completely arbitrary shapes (conductors, dielectrics) you have to use Finite Element Analysis or similar methods.
 
Then, please let me ask the following question: I am really looking for that kind of examples, could you tell me how I can find some examples and solutions related to calculating charge density with finite element analysis ?
 

Similar threads

Graduate Work done via induced charges in a grounded conductor
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Potential of a grounded conductor in the presence of an external charge
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Helmholtz's theorem and charge density
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Why Does Grounding Imply Zero Electric Potential in the Method of Images?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Induced Electrical Field (Maxwell-Faraday's Law)
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Voltage and current waves in a transmission line
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Induced surface charge density
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Relationship between magnetic potential and current density in Maxwell
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad The Method of Images (Electromagnetism)
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad The potential on the rim of a uniformly charged disk
  • · Replies 4 ·
Replies
4
Views
2K