Is the magnetic field inside a solenoid stronger near the border?

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Discussion Overview

The discussion revolves around the behavior of the magnetic field inside a solenoid, specifically whether the magnetic field is stronger near the borders of the solenoid or at its center. Participants explore this question through references to literature, personal intuition, and simulations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant references graphs from a paper and Wikipedia that suggest the magnetic field is stronger near the border of the solenoid, contrasting with their intuition that it should be stronger in the center.
  • Another participant confirms that the magnetic field is indeed strong near the coils, indicating a potential agreement with the initial observation.
  • There is a discussion about the nature of the magnetic field around a long straight wire, noting that the field strength falls off as 1/r, raising questions about the behavior near the coil's center versus its border.
  • One participant asserts that while the field is strongest near the coil, it is most uniform in the center, suggesting a distinction between strength and uniformity.
  • A later reply challenges the intuition by proposing a thought experiment involving increasing the radius of the coil, questioning whether the intuition about the field strength would hold in that scenario.

Areas of Agreement / Disagreement

Participants express differing intuitions regarding the strength of the magnetic field in relation to the solenoid's center and borders. While some acknowledge the observations from literature that support the idea of stronger fields near the borders, others maintain that their intuition suggests the center should be stronger. The discussion remains unresolved with multiple competing views.

Contextual Notes

Participants reference various sources and personal simulations, but there is no consensus on the interpretation of the magnetic field distribution within the solenoid. The discussion includes assumptions about the behavior of magnetic fields in relation to distance from the source coils.

Who May Find This Useful

This discussion may be of interest to those studying electromagnetism, particularly in understanding magnetic field distributions in solenoids and the implications of different configurations.

Rafikix
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I was reading some papers about calculating the magnetic field produced by a coil using the biot savart law and I saw some graphs that caught my attention.

rav.png

This one from a paper from Ravaud, et al. Titled "Calculation of the Magnetic Field Created by a Thick Coil". I saw similar graphs in other articles too.

1611891949303.png


And this one from the wikipedia entry for solenoids.

They seem to indicate that the magnetic field gets stronger near the border, whereas from my intuition I thought they were stronger in the center.
I also did a simulation in python using the biot savart law and the formula from Ravaud's paper and the plot looked like the wikipedia's one, with the magnetic field stronger nearing the border with that triangular shape.

How do I explain this?
 
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By "border" you mean coils? Yes, the field is strong near the coils.
 
Rafikix said:
rav-png.png
The center of the coil is at r=0...that would be about a foot off the side of my monitor. This is in a tenth inch thick wire turn I beleive.
 
Rafikix said:
whereas from my intuition I thought they were stronger in the center.
My intuition is that the coils are the source and the field always gets weaker as you go away from them. I will try to think of a proof.
 
For a long straight wire the field falls off as 1/r. If you get close enough everything is flat...
You mean coil center or wire center ?
 
Rafikix said:
They seem to indicate that the magnetic field gets stronger near the border, whereas from my intuition I thought they were stronger in the center.
The field is most uniform in the center. It is strongest near the coil.
 
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Rafikix said:
... from my intuition I thought they were stronger in the center...
To test intuitions consider extreme cases: Increase the radius of the coil towards infinity while keeping its axial length constant. Does your intuition still say that the field will be strongest in the middle, far far away from the conducting wire loop?
 
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