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 with derivation of electric field of a moving charge'

At first, I derived that: $$\nabla \frac 1{\mu}=-\frac 1{{\mu}^3}\left((1-\beta^2)+\frac{\dot{\vec\beta}\cdot\vec R}c\right)\vec R$$ (dot means differentiation with respect to ##t'##). I assume this result is true because it gives valid result for magnetic field. To find electric field one should also derive partial derivative of ##\vec A## with respect to ##t##. I've used chain rule, substituted ##\vec A## and used derivative of product formula. $$\frac {\partial \vec A}{\partial t}=\frac...
View full post »

Similar threads

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