Helmholtz pair, magnetic field in 3D

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Discussion Overview

The discussion revolves around the visualization and characteristics of the magnetic field generated by Helmholtz coils in three-dimensional space. Participants explore the shape and symmetry of the field, as well as the use of simulation tools to analyze it.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants describe the shape of the magnetic field as resembling a cuboid with arms extending in various directions.
  • Others question the necessity of equations or simulation software to properly address the question posed.
  • There is a suggestion that the field is greatest near the coils and minimal between them, with a more linear field in the center.
  • Participants express uncertainty about the correct terminology for the shape created by the magnetic field between specified limits of the magnetic field strength.
  • Some participants propose that the shape appears mostly cylindrical, while others suggest it could be cuboidal or even a slightly elongated sphere.
  • There is a contention regarding the visual interpretation of the field, with some asserting that it is cylindrically symmetric despite appearances that suggest otherwise.
  • Links to external simulation tools are shared for visualizing the magnetic field generated by the coils.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact shape of the magnetic field or the terminology to describe it. Multiple competing views regarding the geometry and symmetry of the field remain unresolved.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the visual representation of the magnetic field and the dependence on specific definitions of shapes. The discussion also reflects uncertainty about the mathematical modeling of the field.

Sebobo
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New poster has been reminded to always show their work when starting schoolwork threads
Homework Statement
In three dimensions, what shape is the region in which Bx is between 95% and 105% of its value at the centre? Also give the approximate dimensions of this shape.
Relevant Equations
B = (Mu_0 NI)÷R
As far as I can tell, the shape looks like a cuboid with 8 arms pointing in all directions.
 
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Welcome to PF.
If you have no equations then how are you supposed to answer the question?
Will you use a finite element model or simulation software?
 
IMG_20220115_170936.jpg

What is this meant to be in 3d?
 
That looks like the 2D section through the two coils spaced in 3D. The B field is greatest near the wires and minimum between the wires. The field in the centre will be most linear or even.

The way the model and the plot are specified will identify the situation.

Do you understand the Helmholtz coil arrangement ?
 
Yes, that's exactly it... The region in yellow and light green, imagine that in 3D... What name do you give to such a shape?
 
Baluncore said:
That looks like the 2D section through the two coils spaced in 3D. The B field is greatest near the wires and minimum between the wires. The field in the centre will be most linear or even.

The way the model and the plot are specified will identify the situation.

Do you understand the Helmholtz coil arrangement ?
I'm fully aware of the arrangement, I just don't have a clue what you call such a shape that's created by the region's between 0.95 B(0,0) and 1.05 B(0,0)
 
Sebobo said:
I just don't have a clue what you call such a shape that's created by the region's between 0.95 B(0,0) and 1.05 B(0,0)
Seems mostly cylindrical, which is the whole goal of the Helmholtz Coil arrangement.

Do you have access to COMSOL or other simulation software? You could probably extract the field data between those limits and plot it to see how much it deviates from a cylinder.
 
berkeman said:
Seems mostly cylindrical, which is the whole goal of the Helmholtz Coil arrangement.

Do you have access to COMSOL or other simulation software? You could probably extract the field data between those limits and plot it to see how much it deviates from a cylinder.
Cylindrical? Are you sure it's not cuboidal?
 
  • #10
How could a field generated by cylindrical coils be cubical?
 
  • #11
berkeman said:
How could a field generated by cylindrical coils be cubical?
Because I wasn't visualising correctly, are you sure it's not a slightly elongated sphere?
berkeman said:
How could a field generated by cylindrical coils be cubical?
So it's a cylinder with 4 webbed tentacles around it?
 
  • #12
Sebobo said:
So it's a cylinder with 4 webbed tentacles around it?
No, it is cylindrically symmetric. You are just getting fooled by the fact that the side view slice looks like it has 4 of something. But if you mentally rotate the coils along their axis, the slice image does not change. Does that help?
 
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