Laplace Equation Numerical Solution

Click For Summary
The discussion focuses on incorporating point charges into the numerical solution of the Laplace equation. Suggestions include using conformal mapping techniques, particularly through inversion at a specific point. Another proposed method involves modeling the charge as a square and then analyzing the limit as it shrinks to a point. These approaches aim to simplify the complexities involved in point charge scenarios within the Laplace equation framework. The conversation emphasizes innovative mathematical strategies for effective solutions.
jawad hussain
Messages
6
Reaction score
1
Homework Statement
Place a charge of +1 mC at the centre of the square, and initially
using the relaxation method, solve the potentials inside the grid for
the boundary conditions:
• N=S=E=W=10 V
• N=S=10 V; E=W=−10 V
• N=0 V; E=10 V; S=20 V; W=30 V
Relevant Equations
Laplace Equation, Poisson equation
I wonder how to incorporate point charge?
 
Physics news on Phys.org
Perhaps an application of conformal mapping, with an inversion at the point?
Or maybe make it a square too, then take the limit as it shrinks to a point.
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
View full post »

Similar threads

How to Solve the Laplace Equation for Potential Flow Around a Sphere?
  • · Replies 1 ·
Replies
1
Views
1K
Laplace's equation when there is a point dipole
  • · Replies 5 ·
Replies
5
Views
2K
Confused about the nature of Laplace vs Poisson equation in BVP
  • · Replies 11 ·
Replies
11
Views
3K
How Does Equation 4.39 Apply to Dipole Moments in Griffith's Problem 4.37?
  • · Replies 4 ·
Replies
4
Views
3K
Find equilibrium profile T(x) Between Two Rods
  • · Replies 7 ·
Replies
7
Views
2K
Finite element solving of Laplace's equation doesn't converge
  • · Replies 4 ·
Replies
4
Views
2K
3D Laplace solution in Cylindrical Coordinates For a Hollow Cylindrical Tube
  • · Replies 1 ·
Replies
1
Views
3K
Solving Poisson's equation ##\nabla^2\psi##
  • · Replies 30 ·
2
Replies
30
Views
3K
Question about the classic Image Problem
  • · Replies 3 ·
Replies
3
Views
2K
Modeling a spark gap--How to solve a DE with a step function
  • · Replies 3 ·
Replies
3
Views
1K