How to Convert Ampere's Law to Laplace Equations and Solve Numerically?

[yoyobarn]

Homework Statement

I need to write ampere's law (differential form) in the form of Laplace equations / Poisson equations and then solve them numerically using Matlab.

Homework Equations

Del x H = J

The Attempt at a Solution

pls see my attachment


I need help from someone who is good at electromagnetics, and also have some numerical programming background.

Thank you very much for help!

 

[yoyobarn]

Ok now I have come up with code for one wire..

Now i need to code for two wires!

Any idea how to do that?

 

[cragar]

$$\nabla \times B=\mu_0J$$
$$B=\nabla \times A$$
so then we substitute this into amperes law.
$$\nabla \times(\nabla \times A)$$
then we use the vector identity to re-write the curl of the curl.
so we get
$$\nabla(\nabla \cdot A) - (\nabla)^2A=\mu_0J$$
$$\nabla \cdot A = 0$$
I did this in terms of the B field but
$$B=\mu H$$
So now we have reduced this to Poisson equation.
On your second post you said you need code for two wires . well the B fields obey superposition so you can just add the field to the other based on distance.