Magnetic Field Lines Formula (3D)

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SUMMARY

The discussion centers on the complexity of calculating magnetic field lines, particularly for electromagnets and solenoids. It emphasizes that there is no universal formula for magnetic fields; instead, one must solve Maxwell's equations for specific cases. For stationary electromagnetic fields, the Biot-Savart law is applicable, and potential theory provides insights into the behavior of magnetic field lines. The conversation highlights the need for numerical integration techniques to visualize these fields accurately in 3D.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with the Biot-Savart law
  • Knowledge of potential theory
  • Basic programming skills for 3D graphical display
NEXT STEPS
  • Research numerical integration techniques for solving Maxwell's equations
  • Explore the application of the Biot-Savart law in electromagnet design
  • Study potential theory and its relevance to magnetic field visualization
  • Learn programming frameworks for 3D graphics, such as OpenGL or Unity
USEFUL FOR

Physicists, electrical engineers, software developers interested in electromagnetic simulations, and anyone involved in visualizing magnetic fields in 3D.

firemaster
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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.
 
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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...
 
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.
 
firemaster said:
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...
 

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