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fluidistic

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Hello people, in a near future I'd like to calculate (numerically, with finite elements) the magnetic field of several permanent magnets of various shapes. I am wondering which equation(s) I should solve, exactly.

It's been a long time I dived into an EM textbook and I don't have one in hand right now (though I do have internet!).

I think I will have to solve Maxwell equations with the following specifications.

##\vec E=\vec 0## (I consider there is no electric charge anywhere, no electric current either). Futhermore, nothing depends on time (steady state condition, as I won't move the magnets).

This leads to the consideration of ##\nabla \cdot \vec B=0## and ##\nabla \times B = \vec 0##. Now, I do not remember why, but as I remember, it is easier to solve for ##\vec A## the magnetic vector potential given by ##\vec B = \nabla \times \vec A##, to then retrieve ##\vec B##.

However I do not know which kind of boundary conditions I should apply for ##\vec A##. How would I specify that the medium is magnetized?

It's been a long time I dived into an EM textbook and I don't have one in hand right now (though I do have internet!).

I think I will have to solve Maxwell equations with the following specifications.

##\vec E=\vec 0## (I consider there is no electric charge anywhere, no electric current either). Futhermore, nothing depends on time (steady state condition, as I won't move the magnets).

This leads to the consideration of ##\nabla \cdot \vec B=0## and ##\nabla \times B = \vec 0##. Now, I do not remember why, but as I remember, it is easier to solve for ##\vec A## the magnetic vector potential given by ##\vec B = \nabla \times \vec A##, to then retrieve ##\vec B##.

However I do not know which kind of boundary conditions I should apply for ##\vec A##. How would I specify that the medium is magnetized?

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