Graphing magnetic field of two magnets in 3d space

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Discussion Overview

The discussion revolves around the challenge of graphing the magnetic field generated by two magnets located at different coordinates in 3D space. Participants explore methods to determine the point where the magnetic fields from the two magnets cancel each other out, considering various orientations and strengths of the magnets.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in starting the problem of graphing the magnetic field and finding cancellation points, indicating a need for calculus knowledge.
  • Another participant suggests exploiting symmetry in the problem, particularly when magnets are oriented towards each other, and mentions the use of cylindrical coordinates to simplify calculations.
  • There is a concern raised about the complexity introduced by varying orientations of the magnets, such as yaw and pitch angles, which complicates the analysis.
  • A suggestion is made to consider simulation software like ANSYS for visualizing the magnetic fields and finding solutions.
  • One participant proposes using a pole model for the magnets, emphasizing the need to calculate the magnetic field contributions from each magnet separately and combine them to find the total field.
  • Another participant questions what aspects of the problem are confusing, hinting at the complexity of the mathematical expressions involved.

Areas of Agreement / Disagreement

Participants generally agree on the need for a method to analyze the problem, but there are multiple competing views on how to approach the complexity introduced by the magnets' orientations and the mathematical challenges involved. The discussion remains unresolved regarding the best method to graph the fields and find cancellation points.

Contextual Notes

Participants note that the problem's complexity increases with the orientation of the magnets, and there is an acknowledgment of the potential need for computational tools to assist in the analysis. The discussion does not resolve the mathematical steps or assumptions required for a complete solution.

cashflow
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I never figured I would encounter a problem as hard as this. Basically, there are two magnets of varying strength at 2 different x, y, z coordinates. I need to come up with function(s) to graph the field in 3d space. Or, at least find the x,y,z point where the two fields cancel out (if they exist). I know I will need calc iii, but I have no idea where to begin with respect to this problem.
 
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Have you been asked to come up with a general method or do you have a specific problem?

The starting point is your understanding of how magnetic fields interact.

The usual method is to exploit the symmetry of the problem to simplify it. For instance, if the two magnets are pointing right at each other the system has cylindrical symmetry so changing to cylindrical coordinates with the z axis through the magnets simplifies the problem immensely.

To find where the two fields cancel out - you need only write the equations for the field strength at each (x,y,z) point and find the minimum. Note: you also need the orientation and type of the magnets.
 
We just need a general method. The two magnets can be at any location and any orientation (both known), and goal is to find out where the two fields cancel. Anyway, supposing the magnets are oriented towards one another, the problem becomes simple. However, what if one magnet has a 45 degree yaw and 12 degree pitch? The problem becomes confusing and I have no idea where to start... Any formulas I can use as a base to start? Thanks!

This is not for a school project.
 
Last edited by a moderator:
cashflow said:
I never figured I would encounter a problem as hard as this. Basically, there are two magnets of varying strength at 2 different x, y, z coordinates. I need to come up with function(s) to graph the field in 3d space. Or, at least find the x,y,z point where the two fields cancel out (if they exist). I know I will need calc iii, but I have no idea where to begin with respect to this problem.

cashflow said:
We just need a general method. The two magnets can be at any location and any orientation (both known), and goal is to find out where the two fields cancel. Anyway, supposing the magnets are oriented towards one another, the problem becomes simple. However, what if one magnet has a 45 degree yaw and 12 degree pitch? The problem becomes confusing and I have no idea where to start... Any formulas I can use as a base to start? Thanks!

This is not for a school project.

Have you considered getting simulation software like ANSYS?

http://www.ansys.com/Products/Simulation+Technology/Electromagnetics

For general solutions, you may need to simulate the geometries...
 
Last edited by a moderator:
I was going to suggest using a pole model for the magnets, since the setup is not envisaged to be dynamic ...

You have two vectors for each magnet: position and orientation. You can find the field due to each magnet separately OK? You can write an expression for the total field or potential (whichever you like) at some (x,y,z)?

Of course - this is quickly non-trivial.
Which is why we use computers a lot.

Thing is, I don't know what it is that you find "confusing" about this - is it just that the expressions get very complicated?
 

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