Magnetic Field Lines Formula (3D)

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Discussion Overview

The discussion revolves around the challenge of calculating the shape of magnetic field lines, particularly for electromagnets and solenoids, with an interest in creating a 3D graphical display. The scope includes theoretical and practical aspects of magnetic fields and their representation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about a formula for calculating the shape of magnetic field lines for various types of magnets, including solenoids.
  • Another participant notes that calculating magnetic fields becomes complex beyond simple systems and mentions that there are specific formulas for dipoles, infinite lines of current, and infinitely long solenoids, but no general formula exists.
  • A different participant suggests using the Biot-Savart law for calculating fields of electromagnets operating at DC or low frequencies.
  • One participant reiterates the initial inquiry about formulas for magnetic field lines and suggests that while equations exist, they are typically not solvable except in simple cases. They recommend looking into potential theory for stationary cases and mention the concept of lines normal to equipotential surfaces.

Areas of Agreement / Disagreement

Participants express varying levels of agreement on the complexity of calculating magnetic fields, with some acknowledging the existence of specific formulas while others emphasize the lack of a general solution. The discussion remains unresolved regarding a straightforward method for visualizing magnetic field lines.

Contextual Notes

Participants highlight limitations related to the complexity of magnetic field calculations, the need for numerical integration in many cases, and the dependency on specific conditions such as frequency and system geometry.

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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