Magnetic Field Lines Formula (3D)

[firemaster]

Curious as to whether there's a formula for calculating the shape of the magnetic field lines, including electro magnets (solenoids). I want to create a 3D graphical display for the magnetic field lines of magnets.

 

[JesseC]

Calculating magnetic fields for things gets extremely difficult after the simplest of systems. There are formulas for things like dipoles, infinite lines of current, infinitely long solenoids...

There is no "general" magnetic field formula... you'd need to solve Maxwell equation in each case. That would, I imagine need some numerical integration over all space.

But then I don't know much about programming...

 

[Dale]

If you just want to do the field for electromagnets operating at DC or very low frequency then you can use the Biot Savart law.

 

[dgOnPhys]

Curious as to whether there's a formula for calculating the shape of the magnetic field lines, including electro magnets (solenoids). I want to create a 3D graphical display for the magnetic field lines of magnets.

As some have already mentioned it is not that easy but there are equations describing this lines. Not that you would go and solve them (except in very simple cases) but they would provide a way of implementing software to draw them.
Assuming you are interested in stationary (non time-dependent) cases, you can look them up in books dealing with potential theory (Dover? I do not have my books at hand). You are basically dealing with family of lines normal to equipotential surfaces...