Question

I want to calculate the magnetic field from a given image using biot savarts law. For example if I have a picture of a triangle, I say that this triangle forms a closed wire carrying current. Using image derivatives I can get the co-ordinates and direction of the current (normals included). I am struggling implementing this…need a bit of help with logic too. Here is what I have:

Img = imread('littletriangle.bmp');
Img = Img(:,:,1);
Img = double(Img);
[x,y] = size(Img);
[Ix, Iy] = gradient(Img);

biot savart equation is:

b = mu/4*pi sum(Idl x rn / r^2)

where mu/4pi is const, I is current magnitude, rn distance unit vector between a pixel and current, r^2 is the squared magnitude of the displacement between a pixel and the current.

So just to start off, I read the image in, turn it into a binary and then take the image gradient. This gives me the location and orientation of the ‘current’. I now need to calculate the magnetic field from this ‘current’ at every pixel in the image. I am only interested in getting the magnetic field in the x-y plane. anything just to start me off would be brilliant!

Answer 1

For wire

B = mu * I /(2*pi*r)  

B is vector and has. Direction is perpendicular on line between wire an point of interest. Fastest way to rotate vector by 90° is just swapping (x.y) so it becomes (y,x) vector

What about current? If you deal whit current then current is homogenous inside of wire (can be triangle) and I in upper direction is just normalized I per point and per Whole I.

So how to do this?

1. Get current per pixel (current / number of pixel in shape)
2. For each point calculate B using (r calculated form protagora) as sum of all other mini wires expressed as pixel using upper equation. (B is vector and has also direction, so keep track of B as (x,y) )

having picture of 100*100 will yield (100*100)*(100*100) calculations of B equation or something less if you will not calculate filed from empty space.

B is at the end instead of just mu * I /(2*pi*r) sum of all wire and I becomes dI

You do not need to apply any derivatives, just integration (sum)