Helmholtz pair, magnetic field in 3D

[Sebobo]

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.

 

[Baluncore]

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?

 

[Sebobo]

What is this meant to be in 3d?

 

[Baluncore]

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 ?

 

[berkeman]

What is this meant to be in 3d?

Here is a little more intuitive version of that plot:

http://t-sato.in.coocan.jp/compliance/magnetic-field/helmholtz-coil.html

I'm used to a more traditional view, like this:

https://commons.wikimedia.org/wiki/File:Helmholtz_coil_magnetic_field_lines.svg

 

[Sebobo]

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?

 

[Sebobo]

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)

 

[berkeman]

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.

 

[Sebobo]

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?

 

[berkeman]

How could a field generated by cylindrical coils be cubical?

 

[Sebobo]

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?

How could a field generated by cylindrical coils be cubical?

So it's a cylinder with 4 webbed tentacles around it?

 

[berkeman]

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?

 

[robphy]

You might be able to see something with
https://www.falstad.com/vector3dm/
using "Loop Pair Stacked" and Field Vectors, Field Lines, and Magnetic Film

(I never noticed a feature where you can save a URL with the settings.)
https://www.falstad.com/vector3dm/v...d=5&a1=67&a2=53&a3=1&rx=72&ry=-8&rz=50&zm=1.2

 

[berkeman]

(I never noticed a feature where you can save a URL with the settings.)
https://www.falstad.com/vector3dm/v...d=5&a1=67&a2=53&a3=1&rx=72&ry=-8&rz=50&zm=1.2

Awesome! Thanks for posting that.